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A pump can empty a water reservoir in 12 hours. After 4 hours, two more identical pumps are started. What is the total time taken to empty the reservoir?

1. 6 hours 40 minutes
2. 7 hours
3. 8 hours
4. 5 hours 20 minutes

Correct answer: 6 hours 40 minutes

Solution

One pump empties the reservoir in 12 hours, so its rate is 1/12 per hour. In 4 hours, it empties 4/12 = 1/3 of the reservoir; the remaining 2/3 is emptied by 3 pumps together at 3/12 = 1/4 per hour, taking 8/3 hours. Total time = 4 + 8/3 = 20/3 hours = 6 hours 40 minutes.

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