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      Question

      A tank can be filled by pipe A in 6 hours and by pipe B

      in 8 hours. A waste pipe C can empty the full tank in 12 hours. If all three pipes are opened together when the tank is empty, in how many hours will the tank be filled?
      A 7 hours 40 minutes Correct Answer Incorrect Answer
      B 2 hours 49 minutes Correct Answer Incorrect Answer
      C 4 hours 48 minutes Correct Answer Incorrect Answer
      D 4 hours 28 minutes Correct Answer Incorrect Answer

      Solution

      A’s rate = 1/6 tank/hour B’s rate = 1/8 tank/hour C’s (waste) rate = −1/12 tank/hour Net rate = 1/6 + 1/8 − 1/12 LCM of 6, 8, 12 = 24 1/6 = 4/24 1/8 = 3/24 1/12 = 2/24 Net = (4 + 3 − 2)/24 = 5/24 tank/hour Time to fill tank = 1 ÷ (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes.

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