Discussion
A pump can fill a tank with water in 2 hours. Because of a leak, it took \( 2\tfrac{1}{3} \) hours to fill the tank. The leak can drain all the water of the tank in:
Answer: D
Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).
Without the leak the pump fills the tank at \( \tfrac{1}{2} \) per hour; with it, the effective rate is \( \tfrac{3}{7} \) per hour.
\[ \frac{1}{2} - \frac{1}{L} = \frac{1}{7/3} = \frac{3}{7} \]
\[ \frac{1}{L} = \frac{1}{2} - \frac{3}{7} = \frac{7 - 6}{14} = \frac{1}{14} \]
\[ L = 14 \text{ hours} \]
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