A pump can fill a tank with water in 2 hours. Because of a leak, it took \( 2\displaystyle\frac{1}{3} \) hours to fill the tank. In how many hours the leak can drain all the water of the tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 14 hours
In 1 hour the pump alone fills \( \frac{1}{2} \) of the tank. With the leak the tank takes \( 2\frac{1}{3}=\frac{7}{3} \) hours, so in 1 hour it fills \( \frac{3}{7} \) of the tank. The difference is what the leak drains in 1 hour:
\( \displaystyle \frac{1}{2}-\frac{3}{7}=\frac{7-6}{14} \)
\( \displaystyle =\frac{1}{14} \)
So the leak alone drains the full tank in 14 hours.