Question

Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together?

Answer 1

First tap can fill a cistern in 10 hours
Second tap can fill the cistern in 8 hours
Third tap can empty the cistern in 15 hours
$\therefore$ First tap's 1 hour's work $=\frac{1}{10}$
Second tap's 1 hour's work $=\frac{1}{8}$
and third tap's 1 hour's work $=\frac{1}{15}$
If all of them are opened together, then heir one hour's work $=\frac{1}{10}+\frac{1}{8}-\frac{1}{15}$ $=\frac{12+15-8}{120}=\frac{27-8}{120}=\frac{19}{120}$
$\therefore$ They can fill the cistren in $=\frac{120}{19}$ hours $=6\frac{6}{19}$ hours