Question
Pipe A can fill a tank in 12 hours and pipe B can fill
it in 15 hours. A third pipe C can empty a full tank in 20 hours. If all three pipes are opened together, in how many hours will the tank be filled?Solution
Let total work = 1 tank. Rates: A: 1/12 tank/hour B: 1/15 tank/hour C: −1/20 tank/hour (emptying) Net rate = 1/12 + 1/15 − 1/20 LCM of 12, 15, 20 is 60: = (5 + 4 − 3) / 60 = 6/60 = 1/10 tank/hour Time to fill = 1 ÷ (1/10) = 10 hours
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