Discussion
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in .. ?
Answer: D
Work in tanks per hour. The pump alone fills \( \tfrac{1}{2} \); with the leak draining at \( \tfrac{1}{L} \) the net rate fills the tank in \( 2\tfrac{1}{3} = \tfrac{7}{3} \) hours:
\[ \frac{1}{2} - \frac{1}{L} = \frac{3}{7} \]
\[ \frac{1}{L} = \frac{1}{2} - \frac{3}{7} = \frac{7 - 6}{14} = \frac{1}{14} \quad\Longrightarrow\quad L = 14 \text{ hours} \]
A sanity check: the leak costs only 20 minutes over the fill, so it must be far weaker than the pump - a leak emptying the tank in 4 or even 7 hours would be far too strong.
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