Discussion
Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
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).
For the first 3 minutes both taps run:
\[ 3\left(\frac{1}{12} + \frac{1}{15}\right) = 3 \times \frac{5 + 4}{60} = \frac{27}{60} = \frac{9}{20} \]
B alone must supply the remaining \( \tfrac{11}{20} \):
\[ t = \frac{11}{20} \times 15 = 8.25 \text{ min} = 8 \text{ min } 15 \text{ s} \]
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