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