Question

A cistern is filled by one tap in 12 minutes and emptied by another in 10 minutes. If the second pipe is opened 3 minutes after the first, at what time more will the cistern be emptied?

Answer 1

If the volume of cistern = V litres.
Flow rate of tap filling the cistern $=\frac{V}{12}litres/min$
Flow rate of tap filling the cistern $=\frac{V}{10}litres/min$
$\therefore$ In 3 minutes, the cistern is filled $=\frac{V}{12}\times 3litres$ = $\frac{V}{4}litres$
Now both taps are open,
So per minute cistern is filled/emptied is given by $=\frac{V}{12}-\frac{V}{10}=\frac{5V-6V}{60}=-\frac{V}{60}litres/min$
$\therefore \frac{V}{60}$ volume is emptied per minute.
$\therefore \frac{V}{4}$ volume is emptied $=\frac{1}{\frac{y}{60}}\times \frac{6}{4}=\frac{60}{4}=15min$
$\therefore$ cistern will be emptied in 15 minutes.