Question

Pipes A and B can fill an empty tank in $10$ hours and $15$ hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?

Answer 1

Pipe A can fill the tank in $10$ hours

A's one hour's work $=\frac{1}{10}$

Pipe B can fill the tank in $15$ hours.

B's one hour's work $=\frac{1}{15}$

$\therefore$ A and B's one hour's work $=\frac{1}{10}+\frac{1}{15}$

$=\frac{1\times 3}{10\times 3}+\frac{1\times 2}{15\times 2}$ [L.C.M of $10$ and $15$ is $30$]

$=\frac{3}{30}+\frac{2}{30}$

$=\frac{3+2}{30}$

$=\frac{5}{30}=\frac{1}{6}$

$\therefore$ A's and B's one hour's work $=\frac{1}{6}$

$\therefore$ Pipes A and B can fill the empty tank in $6$ hours.