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?
Solution:
Time taken by the first tap to fill the cistern $=8$ hours
Time taken by the second tap to fill the cistern $=4$ hours
$\therefore$ Work done by the first tap in 1 hour $=\frac{1}{8}$
Work done by the second tap in 1 hour $=\frac{1}{4}$
$\therefore$ Work done by both the taps in 1 hour $=\frac{1}{8}+\frac{1}{4}$
$=\frac{1+2}{8}=\frac{3}{8}$
Thus, both the taps together will fill the cistern in $\frac{8}{3}$ hours or $2 \frac{2}{3}$ hours.