Question

Two pipes can fill a cistern in 9 hours and 12 hours respectively. In how much time they fill the cistern when opened together?

Answer 1

36/7 hr will be the answer

Answer 2

let x and y be the time taken to fill the tanks separately. then,
$\frac{1}{x} = \frac{1}{9} \: \: \: \: ... \frac{1}{12} = \frac{1}{y}$
then let z be the time taken by them to fill the tank together.where
$\frac{1}{z} = \frac{1}{x} + \frac{1}{y} \\= \frac{1}{9} + \frac{1}{12} \\ = \frac{4 + 3}{36} \\ \frac{1}{z} = \frac{7}{36} \\ z =36/7\: or 5 \: \: \: {approximately}$