Question
A tank can be filled by pipe A in 12 hours and by pipe B
in 18 hours. A waste pipe C can empty the full tank in 36 hours. If all three pipes are opened together, in how many hours will the tank be filled?Solution
A’s rate = 1/12 tank/hour B’s rate = 1/18 tank/hour C’s (waste) rate = −1/36 tank/hour Net rate = 1/12 + 1/18 − 1/36 LCM of 12, 18, 36 is 36: 1/12 = 3/36 1/18 = 2/36 1/36 = 1/36 Net = (3 + 2 − 1)/36 = 4/36 = 1/9 Time = 1 ÷ (1/9) = 9 hours Answer: 9 hours.
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