Discussion
Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 minutes?
Answer: C
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).
A runs for the whole 18 minutes:
\[ \frac{18}{24} = \frac{3}{4} \text{ of the tank} \]
B must supply the remaining \( \tfrac{1}{4} \) at \( \tfrac{1}{32} \) per minute:
\[ t = \frac{1}{4} \times 32 = 8 \text{ minutes} \]
So B is closed after 8 minutes.
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