Question

Tick (✓) the correct answer:
A pump can fill a tank in 2 hours. Due to a leak in the tank it takes $2\frac{1}{3}$ hours to fill the tank. The leak can empty the full tank in
(a) $2\frac{1}{3}$ hours
(b) 7 hours
(c) 8 hours
(d) 14 hours

Answer 1

(d) 14 hours

$$\begin{gathered} \mathrm{A}\mathrm{pump}\mathrm{can}\mathrm{fill}\mathrm{a}\mathrm{tank}\mathrm{in}2\mathrm{hours}. \\ \text{Part of the tank filled by the pump in one hour}=\frac{1}{2} \\ \text{Suppose}\mathrm{the}\mathrm{leak}\text{empties}\mathrm{a}\mathrm{full}\mathrm{tank}\mathrm{in}\mathrm{x}\mathrm{hours}. \\ \text{Part of the tank emptied by the leak in one hour}=-\frac{1}{\mathrm{x}} \\ \text{Part of tank filled in one hour}=\frac{1}{2}-\frac{1}{\mathrm{x}}=\frac{3}{7}\left(\mathrm{given}\right) \\ \frac{1}{\mathrm{x}}=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14} \\ \mathrm{x}=14\mathrm{hours} \end{gathered}$$