Discussion
A cistern is filled by Pipe A and Pipe B together in 2.4 hours. Pipe A alone can fill the cistern at the rate of 100 litres per hour. Pipe B alone can fill the cistern in 4 hours. What is the capacity of the cistern?
Answer: B
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).
\[ \text{A's rate} = \frac{1}{2.4} - \frac{1}{4} = \frac{5 - 3}{12} = \frac{1}{6} \]
So A alone would fill the cistern in 6 hours. At 100 litres an hour:
\[ \text{capacity} = 6 \times 100 = 600 \text{ litres} \]
Pipe B's own time is only needed to isolate A's rate; the capacity then follows from A's known flow.
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