Question 1 of 201

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The lowest common multiple of 9, 12, 27, 36, 54 \begin{align*} \frac{9}{5} &= \frac{108}{60}, \ \frac{12}{7}=\frac{108}{63} \\ \frac{27}{17} &= \frac{108}{68}, \ \frac{36}{19} = \frac{108}{57} \\ \frac{54}{29} &= \frac{108}{58} \end{align*}

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 21\text{ days} = \frac{1}{2} \text{ of work.} \end{equation} So $\frac{1}{2}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{2} \end{equation} so number of days $=\frac{1}{2}\times 42 = 21$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 22\text{ days} = \frac{11}{21} \text{ of work.} \end{equation} So $\frac{10}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{10}{21} \end{equation} so number of days $=\frac{10}{21}\times 42 = 20$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 23\text{ days} = \frac{23}{42} \text{ of work.} \end{equation} So $\frac{19}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{19}{42} \end{equation} so number of days $=\frac{19}{42}\times 42 = 19$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 24\text{ days} = \frac{4}{7} \text{ of work.} \end{equation} So $\frac{3}{7}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{3}{7} \end{equation} so number of days $=\frac{3}{7}\times 42 = 18$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 25\text{ days} = \frac{25}{42} \text{ of work.} \end{equation} So $\frac{17}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{17}{42} \end{equation} so number of days $=\frac{17}{42}\times 42 = 17$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 26\text{ days} = \frac{13}{21} \text{ of work.} \end{equation} So $\frac{8}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{8}{21} \end{equation} so number of days $=\frac{8}{21}\times 42 = 16$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 27\text{ days} = \frac{9}{14} \text{ of work.} \end{equation} So $\frac{5}{14}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{5}{14} \end{equation} so number of days $=\frac{5}{14}\times 42 = 15$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 28\text{ days} = \frac{2}{3} \text{ of work.} \end{equation} So $\frac{1}{3}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{3} \end{equation} so number of days $=\frac{1}{3}\times 42 = 14$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 29\text{ days} = \frac{29}{42} \text{ of work.} \end{equation} So $\frac{13}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{13}{42} \end{equation} so number of days $=\frac{13}{42}\times 42 = 13$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 30\text{ days} = \frac{5}{7} \text{ of work.} \end{equation} So $\frac{2}{7}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{2}{7} \end{equation} so number of days $=\frac{2}{7}\times 42 = 12$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 31\text{ days} = \frac{31}{42} \text{ of work.} \end{equation} So $\frac{11}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{11}{42} \end{equation} so number of days $=\frac{11}{42}\times 42 = 11$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 32\text{ days} = \frac{16}{21} \text{ of work.} \end{equation} So $\frac{5}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{5}{21} \end{equation} so number of days $=\frac{5}{21}\times 42 = 10$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 33\text{ days} = \frac{11}{14} \text{ of work.} \end{equation} So $\frac{3}{14}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{3}{14} \end{equation} so number of days $=\frac{3}{14}\times 42 = 9$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 34\text{ days} = \frac{17}{21} \text{ of work.} \end{equation} So $\frac{4}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{4}{21} \end{equation} so number of days $=\frac{4}{21}\times 42 = 8$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 35\text{ days} = \frac{5}{6} \text{ of work.} \end{equation} So $\frac{1}{6}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{6} \end{equation} so number of days $=\frac{1}{6}\times 42 = 7$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 36\text{ days} = \frac{6}{7} \text{ of work.} \end{equation} So $\frac{1}{7}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{7} \end{equation} so number of days $=\frac{1}{7}\times 42 = 6$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 37\text{ days} = \frac{37}{42} \text{ of work.} \end{equation} So $\frac{5}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{5}{42} \end{equation} so number of days $=\frac{5}{42}\times 42 = 5$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 38\text{ days} = \frac{19}{21} \text{ of work.} \end{equation} So $\frac{2}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{2}{21} \end{equation} so number of days $=\frac{2}{21}\times 42 = 4$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 39\text{ days} = \frac{13}{14} \text{ of work.} \end{equation} So $\frac{1}{14}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{14} \end{equation} so number of days $=\frac{1}{14}\times 42 = 3$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 40\text{ days} = \frac{20}{21} \text{ of work.} \end{equation} So $\frac{1}{21}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{21} \end{equation} so number of days $=\frac{1}{21}\times 42 = 2$.

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\begin{align*} \text{22 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $B$ does $1/42$ work. \begin{equation} A: 21 \times 2 / 1 = 42 \text{ days alone,} \end{equation} so in one day $A$ does $1/42$ work $($or $1/21-1/42=1/42)$. \begin{equation} A: 1/42 \times 41\text{ days} = \frac{41}{42} \text{ of work.} \end{equation} So $\frac{1}{42}$ of work left for $B$. \begin{equation} B: 1/42 \times \text{ number of days } = \frac{1}{42} \end{equation} so number of days $=\frac{1}{42}\times 42 = 1$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 21\text{ days} = \frac{1}{4} \text{ of work.} \end{equation} So $\frac{3}{4}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{3}{4} \end{equation} so number of days $=\frac{3}{4}\times 28 = 21$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 24\text{ days} = \frac{2}{7} \text{ of work.} \end{equation} So $\frac{5}{7}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{5}{7} \end{equation} so number of days $=\frac{5}{7}\times 28 = 20$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 27\text{ days} = \frac{9}{28} \text{ of work.} \end{equation} So $\frac{19}{28}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{19}{28} \end{equation} so number of days $=\frac{19}{28}\times 28 = 19$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 30\text{ days} = \frac{5}{14} \text{ of work.} \end{equation} So $\frac{9}{14}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{9}{14} \end{equation} so number of days $=\frac{9}{14}\times 28 = 18$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 33\text{ days} = \frac{11}{28} \text{ of work.} \end{equation} So $\frac{17}{28}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{17}{28} \end{equation} so number of days $=\frac{17}{28}\times 28 = 17$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 36\text{ days} = \frac{3}{7} \text{ of work.} \end{equation} So $\frac{4}{7}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{4}{7} \end{equation} so number of days $=\frac{4}{7}\times 28 = 16$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 39\text{ days} = \frac{13}{28} \text{ of work.} \end{equation} So $\frac{15}{28}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{15}{28} \end{equation} so number of days $=\frac{15}{28}\times 28 = 15$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 42\text{ days} = \frac{1}{2} \text{ of work.} \end{equation} So $\frac{1}{2}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{1}{2} \end{equation} so number of days $=\frac{1}{2}\times 28 = 14$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 45\text{ days} = \frac{15}{28} \text{ of work.} \end{equation} So $\frac{13}{28}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{13}{28} \end{equation} so number of days $=\frac{13}{28}\times 28 = 13$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:3$. $1+3=4$. \begin{equation} B : 21 \times 4 / 3 = 28 \text{ days alone,} \end{equation} so in one day $B$ does $1/28$ work. \begin{equation} A: 21 \times 4 / 1 = 84 \text{ days alone,} \end{equation} so in one day $A$ does $1/84$ work $($or $1/21-1/28=1/84)$. \begin{equation} A: 1/84 \times 48\text{ days} = \frac{4}{7} \text{ of work.} \end{equation} So $\frac{3}{7}$ of work left for $B$. \begin{equation} B: 1/28 \times \text{ number of days } = \frac{3}{7} \end{equation} so number of days $=\frac{3}{7}\times 28 = 12$.

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\begin{align*} \text{28 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:7$. $1+7=8$. \begin{equation} B : 21 \times 8 / 7 = 24 \text{ days alone,} \end{equation} so in one day $B$ does $1/24$ work. \begin{equation} A: 21 \times 8 / 1 = 168 \text{ days alone,} \end{equation} so in one day $A$ does $1/168$ work $($or $1/21-1/24=1/168)$. \begin{equation} A: 1/168 \times 21\text{ days} = \frac{1}{8} \text{ of work.} \end{equation} So $\frac{7}{8}$ of work left for $B$. \begin{equation} B: 1/24 \times \text{ number of days } = \frac{7}{8} \end{equation} so number of days $=\frac{7}{8}\times 24 = 21$.

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\begin{align*} \text{28 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:7$. $1+7=8$. \begin{equation} B : 21 \times 8 / 7 = 24 \text{ days alone,} \end{equation} so in one day $B$ does $1/24$ work. \begin{equation} A: 21 \times 8 / 1 = 168 \text{ days alone,} \end{equation} so in one day $A$ does $1/168$ work $($or $1/21-1/24=1/168)$. \begin{equation} A: 1/168 \times 28\text{ days} = \frac{1}{6} \text{ of work.} \end{equation} So $\frac{5}{6}$ of work left for $B$. \begin{equation} B: 1/24 \times \text{ number of days } = \frac{5}{6} \end{equation} so number of days $=\frac{5}{6}\times 24 = 20$.

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\begin{align*} \text{28 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:7$. $1+7=8$. \begin{equation} B : 21 \times 8 / 7 = 24 \text{ days alone,} \end{equation} so in one day $B$ does $1/24$ work. \begin{equation} A: 21 \times 8 / 1 = 168 \text{ days alone,} \end{equation} so in one day $A$ does $1/168$ work $($or $1/21-1/24=1/168)$. \begin{equation} A: 1/168 \times 35\text{ days} = \frac{5}{24} \text{ of work.} \end{equation} So $\frac{19}{24}$ of work left for $B$. \begin{equation} B: 1/24 \times \text{ number of days } = \frac{19}{24} \end{equation} so number of days $=\frac{19}{24}\times 24 = 19$.

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\begin{align*} \text{28 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:7$. $1+7=8$. \begin{equation} B : 21 \times 8 / 7 = 24 \text{ days alone,} \end{equation} so in one day $B$ does $1/24$ work. \begin{equation} A: 21 \times 8 / 1 = 168 \text{ days alone,} \end{equation} so in one day $A$ does $1/168$ work $($or $1/21-1/24=1/168)$. \begin{equation} A: 1/168 \times 42\text{ days} = \frac{1}{4} \text{ of work.} \end{equation} So $\frac{3}{4}$ of work left for $B$. \begin{equation} B: 1/24 \times \text{ number of days } = \frac{3}{4} \end{equation} so number of days $=\frac{3}{4}\times 24 = 18$.

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\begin{align*} \text{28 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:7$. $1+7=8$. \begin{equation} B : 21 \times 8 / 7 = 24 \text{ days alone,} \end{equation} so in one day $B$ does $1/24$ work. \begin{equation} A: 21 \times 8 / 1 = 168 \text{ days alone,} \end{equation} so in one day $A$ does $1/168$ work $($or $1/21-1/24=1/168)$. \begin{equation} A: 1/168 \times 49\text{ days} = \frac{7}{24} \text{ of work.} \end{equation} So $\frac{17}{24}$ of work left for $B$. \begin{equation} B: 1/24 \times \text{ number of days } = \frac{17}{24} \end{equation} so number of days $=\frac{17}{24}\times 24 = 17$.

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\begin{align*} \text{42 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:21$. $1+21=22$. \begin{equation} B : 21 \times 22 / 21 = 22 \text{ days alone,} \end{equation} so in one day $B$ does $1/22$ work. \begin{equation} A: 21 \times 22 / 1 = 462 \text{ days alone,} \end{equation} so in one day $A$ does $1/462$ work $($or $1/21-1/22=1/462)$. \begin{equation} A: 1/462 \times 21\text{ days} = \frac{1}{22} \text{ of work.} \end{equation} So $\frac{21}{22}$ of work left for $B$. \begin{equation} B: 1/22 \times \text{ number of days } = \frac{21}{22} \end{equation} so number of days $=\frac{21}{22}\times 22 = 21$.

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\begin{align*} \text{42 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{21 days by }A + 21\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:21$. $1+21=22$. \begin{equation} B : 21 \times 22 / 21 = 22 \text{ days alone,} \end{equation} so in one day $B$ does $1/22$ work. \begin{equation} A: 21 \times 22 / 1 = 462 \text{ days alone,} \end{equation} so in one day $A$ does $1/462$ work $($or $1/21-1/22=1/462)$. \begin{equation} A: 1/462 \times 42\text{ days} = \frac{1}{11} \text{ of work.} \end{equation} So $\frac{10}{11}$ of work left for $B$. \begin{equation} B: 1/22 \times \text{ number of days } = \frac{10}{11} \end{equation} so number of days $=\frac{10}{11}\times 22 = 20$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 20\text{ days} = \frac{20}{33} \text{ of work.} \end{equation} So $\frac{13}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{13}{33} \end{equation} so number of days $=\frac{13}{33}\times 66 = 26$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 21\text{ days} = \frac{7}{11} \text{ of work.} \end{equation} So $\frac{4}{11}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{4}{11} \end{equation} so number of days $=\frac{4}{11}\times 66 = 24$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 22\text{ days} = \frac{2}{3} \text{ of work.} \end{equation} So $\frac{1}{3}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{1}{3} \end{equation} so number of days $=\frac{1}{3}\times 66 = 22$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 23\text{ days} = \frac{23}{33} \text{ of work.} \end{equation} So $\frac{10}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{10}{33} \end{equation} so number of days $=\frac{10}{33}\times 66 = 20$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 24\text{ days} = \frac{8}{11} \text{ of work.} \end{equation} So $\frac{3}{11}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{3}{11} \end{equation} so number of days $=\frac{3}{11}\times 66 = 18$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 25\text{ days} = \frac{25}{33} \text{ of work.} \end{equation} So $\frac{8}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{8}{33} \end{equation} so number of days $=\frac{8}{33}\times 66 = 16$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 26\text{ days} = \frac{26}{33} \text{ of work.} \end{equation} So $\frac{7}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{7}{33} \end{equation} so number of days $=\frac{7}{33}\times 66 = 14$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 27\text{ days} = \frac{9}{11} \text{ of work.} \end{equation} So $\frac{2}{11}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{2}{11} \end{equation} so number of days $=\frac{2}{11}\times 66 = 12$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 28\text{ days} = \frac{28}{33} \text{ of work.} \end{equation} So $\frac{5}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{5}{33} \end{equation} so number of days $=\frac{5}{33}\times 66 = 10$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 29\text{ days} = \frac{29}{33} \text{ of work.} \end{equation} So $\frac{4}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{4}{33} \end{equation} so number of days $=\frac{4}{33}\times 66 = 8$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 30\text{ days} = \frac{10}{11} \text{ of work.} \end{equation} So $\frac{1}{11}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{1}{11} \end{equation} so number of days $=\frac{1}{11}\times 66 = 6$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 31\text{ days} = \frac{31}{33} \text{ of work.} \end{equation} So $\frac{2}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{2}{33} \end{equation} so number of days $=\frac{2}{33}\times 66 = 4$.

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\begin{align*} \text{23 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=2:1$. $2+1=3$. \begin{equation} B : 22 \times 3 / 1 = 66 \text{ days alone,} \end{equation} so in one day $B$ does $1/66$ work. \begin{equation} A: 22 \times 3 / 2 = 33 \text{ days alone,} \end{equation} so in one day $A$ does $1/33$ work $($or $1/22-1/66=1/33)$. \begin{equation} A: 1/33 \times 32\text{ days} = \frac{32}{33} \text{ of work.} \end{equation} So $\frac{1}{33}$ of work left for $B$. \begin{equation} B: 1/66 \times \text{ number of days } = \frac{1}{33} \end{equation} so number of days $=\frac{1}{33}\times 66 = 2$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 20\text{ days} = \frac{5}{11} \text{ of work.} \end{equation} So $\frac{6}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{6}{11} \end{equation} so number of days $=\frac{6}{11}\times 44 = 24$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 21\text{ days} = \frac{21}{44} \text{ of work.} \end{equation} So $\frac{23}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{23}{44} \end{equation} so number of days $=\frac{23}{44}\times 44 = 23$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 22\text{ days} = \frac{1}{2} \text{ of work.} \end{equation} So $\frac{1}{2}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{2} \end{equation} so number of days $=\frac{1}{2}\times 44 = 22$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 23\text{ days} = \frac{23}{44} \text{ of work.} \end{equation} So $\frac{21}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{21}{44} \end{equation} so number of days $=\frac{21}{44}\times 44 = 21$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 24\text{ days} = \frac{6}{11} \text{ of work.} \end{equation} So $\frac{5}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{5}{11} \end{equation} so number of days $=\frac{5}{11}\times 44 = 20$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 25\text{ days} = \frac{25}{44} \text{ of work.} \end{equation} So $\frac{19}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{19}{44} \end{equation} so number of days $=\frac{19}{44}\times 44 = 19$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 26\text{ days} = \frac{13}{22} \text{ of work.} \end{equation} So $\frac{9}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{9}{22} \end{equation} so number of days $=\frac{9}{22}\times 44 = 18$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 27\text{ days} = \frac{27}{44} \text{ of work.} \end{equation} So $\frac{17}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{17}{44} \end{equation} so number of days $=\frac{17}{44}\times 44 = 17$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 28\text{ days} = \frac{7}{11} \text{ of work.} \end{equation} So $\frac{4}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{4}{11} \end{equation} so number of days $=\frac{4}{11}\times 44 = 16$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 29\text{ days} = \frac{29}{44} \text{ of work.} \end{equation} So $\frac{15}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{15}{44} \end{equation} so number of days $=\frac{15}{44}\times 44 = 15$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 30\text{ days} = \frac{15}{22} \text{ of work.} \end{equation} So $\frac{7}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{7}{22} \end{equation} so number of days $=\frac{7}{22}\times 44 = 14$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 31\text{ days} = \frac{31}{44} \text{ of work.} \end{equation} So $\frac{13}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{13}{44} \end{equation} so number of days $=\frac{13}{44}\times 44 = 13$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 32\text{ days} = \frac{8}{11} \text{ of work.} \end{equation} So $\frac{3}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{3}{11} \end{equation} so number of days $=\frac{3}{11}\times 44 = 12$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 33\text{ days} = \frac{3}{4} \text{ of work.} \end{equation} So $\frac{1}{4}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{4} \end{equation} so number of days $=\frac{1}{4}\times 44 = 11$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 34\text{ days} = \frac{17}{22} \text{ of work.} \end{equation} So $\frac{5}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{5}{22} \end{equation} so number of days $=\frac{5}{22}\times 44 = 10$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 35\text{ days} = \frac{35}{44} \text{ of work.} \end{equation} So $\frac{9}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{9}{44} \end{equation} so number of days $=\frac{9}{44}\times 44 = 9$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 36\text{ days} = \frac{9}{11} \text{ of work.} \end{equation} So $\frac{2}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{2}{11} \end{equation} so number of days $=\frac{2}{11}\times 44 = 8$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 37\text{ days} = \frac{37}{44} \text{ of work.} \end{equation} So $\frac{7}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{7}{44} \end{equation} so number of days $=\frac{7}{44}\times 44 = 7$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 38\text{ days} = \frac{19}{22} \text{ of work.} \end{equation} So $\frac{3}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{3}{22} \end{equation} so number of days $=\frac{3}{22}\times 44 = 6$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 39\text{ days} = \frac{39}{44} \text{ of work.} \end{equation} So $\frac{5}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{5}{44} \end{equation} so number of days $=\frac{5}{44}\times 44 = 5$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 40\text{ days} = \frac{10}{11} \text{ of work.} \end{equation} So $\frac{1}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{11} \end{equation} so number of days $=\frac{1}{11}\times 44 = 4$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 41\text{ days} = \frac{41}{44} \text{ of work.} \end{equation} So $\frac{3}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{3}{44} \end{equation} so number of days $=\frac{3}{44}\times 44 = 3$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 42\text{ days} = \frac{21}{22} \text{ of work.} \end{equation} So $\frac{1}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{22} \end{equation} so number of days $=\frac{1}{22}\times 44 = 2$.

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\begin{align*} \text{23 days by }A + 21\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 43\text{ days} = \frac{43}{44} \text{ of work.} \end{equation} So $\frac{1}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{44} \end{equation} so number of days $=\frac{1}{44}\times 44 = 1$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 20\text{ days} = \frac{5}{11} \text{ of work.} \end{equation} So $\frac{6}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{6}{11} \end{equation} so number of days $=\frac{6}{11}\times 44 = 24$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 21\text{ days} = \frac{21}{44} \text{ of work.} \end{equation} So $\frac{23}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{23}{44} \end{equation} so number of days $=\frac{23}{44}\times 44 = 23$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 22\text{ days} = \frac{1}{2} \text{ of work.} \end{equation} So $\frac{1}{2}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{2} \end{equation} so number of days $=\frac{1}{2}\times 44 = 22$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 23\text{ days} = \frac{23}{44} \text{ of work.} \end{equation} So $\frac{21}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{21}{44} \end{equation} so number of days $=\frac{21}{44}\times 44 = 21$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 24\text{ days} = \frac{6}{11} \text{ of work.} \end{equation} So $\frac{5}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{5}{11} \end{equation} so number of days $=\frac{5}{11}\times 44 = 20$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 25\text{ days} = \frac{25}{44} \text{ of work.} \end{equation} So $\frac{19}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{19}{44} \end{equation} so number of days $=\frac{19}{44}\times 44 = 19$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 26\text{ days} = \frac{13}{22} \text{ of work.} \end{equation} So $\frac{9}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{9}{22} \end{equation} so number of days $=\frac{9}{22}\times 44 = 18$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 27\text{ days} = \frac{27}{44} \text{ of work.} \end{equation} So $\frac{17}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{17}{44} \end{equation} so number of days $=\frac{17}{44}\times 44 = 17$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 28\text{ days} = \frac{7}{11} \text{ of work.} \end{equation} So $\frac{4}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{4}{11} \end{equation} so number of days $=\frac{4}{11}\times 44 = 16$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 29\text{ days} = \frac{29}{44} \text{ of work.} \end{equation} So $\frac{15}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{15}{44} \end{equation} so number of days $=\frac{15}{44}\times 44 = 15$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 30\text{ days} = \frac{15}{22} \text{ of work.} \end{equation} So $\frac{7}{22}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{7}{22} \end{equation} so number of days $=\frac{7}{22}\times 44 = 14$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 31\text{ days} = \frac{31}{44} \text{ of work.} \end{equation} So $\frac{13}{44}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{13}{44} \end{equation} so number of days $=\frac{13}{44}\times 44 = 13$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 32\text{ days} = \frac{8}{11} \text{ of work.} \end{equation} So $\frac{3}{11}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{3}{11} \end{equation} so number of days $=\frac{3}{11}\times 44 = 12$.

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\begin{align*} \text{24 days by }A + 20\text{ days by }B &= 1 \text{ project} \\ \text{22 days by }A + 22\text{ days by }B &= 1 \text{ project} \end{align*} Solve above 2 equations get ratio $A:B=1:1$. $1+1=2$. \begin{equation} B : 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $B$ does $1/44$ work. \begin{equation} A: 22 \times 2 / 1 = 44 \text{ days alone,} \end{equation} so in one day $A$ does $1/44$ work $($or $1/22-1/44=1/44)$. \begin{equation} A: 1/44 \times 33\text{ days} = \frac{3}{4} \text{ of work.} \end{equation} So $\frac{1}{4}$ of work left for $B$. \begin{equation} B: 1/44 \times \text{ number of days } = \frac{1}{4} \end{equation} so number of days $=\frac{1}{4}\times 44 = 11$.