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in Commercial Mathematics by (31.2k points)
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A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?

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Number of days A required do a piece of work : 9 days 

Let number of days B required do a piece of work : X days 

Number of hours required by A and B together to do a piece of work : 6 days

Work done by A in one day: \(\frac{1}{9}\)

Work done by B in one day: \(\frac{1}{x}\)

Work done by A and B together in a day : \(\frac{1}{6}\)

Work done by A and B together in one day : \(\frac{1}{9}+\frac{1}{x}=\frac{x\,+\,9}{9x}=\frac{1}{6}\)

\(\therefore \frac{x\,+\,9}{9x}=\frac{1}{6}\)

⇒ 6X + 54 = 9X 

⇒ 3X = 54 

⇒ X = 54/3 = 18 

∴ B can do the work 18 days

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