Question
Pipe A can fill a tank in 6 hours, and Pipe B can fill
it in 8 hours. Pipe C can empty the tank in 10 hours. If all three pipes are opened simultaneously, how long will it take to fill the tank?Solution
Rate of Pipe A = 1/6, Rate of Pipe B = 1/8, Rate of Pipe C = -1/10 Net rate when all three are open = 1/6 + 1/8 - 1/10 Net rate = (40 + 30 - 24) / 240 = 46 / 240 = 23 / 120 Time to fill the tank = 1 / (Net rate) = 120 / 23 ≈ 5.22 hours Correct Option: b) 5.22 hours
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