Question
Ā Pipe A can fill a tank in 12 hours, pipe B in 15
hours, and an outlet pipe C can empty a full tank in 10 hours. All three are opened together. After 3 hours, pipe C is closed. How much more time will A and B take to fill the tank completely?Solution
Rates in tank/day (take āunit tankā): Aās rate = 1/12 Bās rate = 1/15 Cās rate = ā1/10 (emptying) Net rate (A + B + C) = 1/12 + 1/15 ā 1/10 LCM of 12, 15, 10 is 60: = (5 + 4 ā 6) / 60 = 3/60 = 1/20 tank/hour Work done in first 3 hours = 3 Ć (1/20) = 3/20 of tank. Remaining = 1 ā 3/20 = 17/20 of tank. After C is closed, only A and B work: (A + B) rate = 1/12 + 1/15 = (5 + 4) / 60 = 9/60 = 3/20 tank/hour Time to finish remaining work = (17/20) Ć· (3/20) = 17/3 hours.
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