Discussion
Two pipes M and N can fill a tank in 22.5 and 15 minutes, respectively. If both the pipes are opened simultaneously, after how much time should N be closed so that the tank is full in 18 minutes?
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).
M runs for the whole 18 minutes:
\[ \frac{18}{22.5} = 0.8 \text{ of the tank} \]
N must supply the remaining 0.2 at a rate of \( \tfrac{1}{15} \) per minute:
\[ t = 0.2 \times 15 = 3 \text{ minutes} \]
So N is closed after 3 minutes. The question asks when N stops, not how long it is shut for.
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