Question

A cistern can be filled by one tap in $8$ hours, and by another in $4$ hours. How long will it take to fill the cistern if both taps are opened together?

Answer 1

First tap's $1$ hour work to fill the cistern $=\frac{1}{8}$

Second tap's $1$ hour work to fill the cistern$=\frac{1}{4}$

Both's $1$ hour work $=\frac{1}{8}+\frac{1}{4}$
$=\frac{1+2}{8}$
$=\frac{3}{8}$
Therefore, both taps will fill the cistern in $\frac{8}{3}=2\frac{2}{3}$ hours.