Question
A tank can be filled by pipe A in 6 hours and by pipe B
in 8 hours. A third pipe C can empty the tank in 12 hours. If all three pipes are opened together, in how many hours will the tank be filled?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(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 = 1 ÷ (5/24) = 24/5 hours Answer: 24/5 hours.
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