Tap A can drain a cistern in 24 hours, while Tap B can do the same in 36 hours. Tap A and B are opened simultaneously, and B works at 100% and 60% efficiency at alternate hours. Find the time required to drain the cistern.

15(13 / 21)
15(17 / 21)
14(3 / 5)
16(11 / 21)

Correct answer: 15(13 / 21)

Solution

A drains at $1/24$ tank per hour and B at $1/36$ tank per hour. Since B alternates between 100% and 60% efficiency, its average over 2 hours is $\frac{1}{36}+\frac{0.6}{36}$ per hour in alternating hours, and the combined work can be tracked in cycles to get the total time as $15\frac{13}{21}$ hours.

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