Discussion
A tap can fill a tub in 24 hours. Due to a leak at the bottom of the tub, the tap fills the tub in 36 hours. If the tub is full, how much time will the leak take to empty it?
Answer: A
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).
\[ \frac{1}{24} - \frac{1}{L} = \frac{1}{36} \]
\[ \frac{1}{L} = \frac{3 - 2}{72} = \frac{1}{72} \quad\Longrightarrow\quad L = 72 \text{ hours} \]
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