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Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

Correct answer: C. 20 hrs

  • A. 25 hrs
  • B. 28 hrs
  • C. 20 hrs
  • D. 35 hrs

Explanation

Let the faster pipe take x hours, so the slower pipe takes x + 10 hours. Their combined rate gives 1/x + 1/(x + 10) = 1/12, so 12(2x + 10) = x(x + 10), leading to x² - 14x - 120 = 0 and x = 20 hours. The likely trap is 28 hours, which comes from setting up the rate equation incorrectly.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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