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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?

Correct answer: C. 120 gallons

  • A. 60 gallons
  • B. 100 gallons
  • C. 120 gallons
  • D. 180 gallons

Explanation

The two filling pipes together have rate 1/20 + 1/24 = 11/120 tank per minute, while all three together fill at 1/15 = 8/120 tank per minute. Thus the waste pipe reduces the rate by 3/120 = 1/40 tank per minute, and this equals 3 gallons per minute, so the capacity is 3 divided by 1/40 = 120 gallons. The likely mistake is choosing 60 gallons by using only one filling pipe's rate.

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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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