Question

One tap can fill a cistern in 3 hours and the waste pipe can empty the full cistern in 5 hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?

Answer 1

One tap can fill a cistern in = 3 hours
Waste pipe can empty a cistern in = 5 hours
$\therefore$ One tap 1 hour work $=\frac{1}{3}$
Waste pipe 1 hour work $=\frac{1}{5}$
$\therefore$ One tap and waste pipe together 1 hour work
$=\frac{1}{3}-\frac{1}{5}=\frac{5-3}{15}$
$=\frac{2}{15}$
$\therefore$ Empty cistern will be full in $=\frac{15}{2}$ hours
$=7\frac{1}{2}$ hours.