Question
Two pipes X and Y can fill an empty tank in 8 hours and
10 hours, respectively. Pipe Z alone can empty the completely filled tank in 15 hours. Firstly, both pipes X and Y are opened, and after 4 hours, pipe Z is also opened. What will be the total time (in hours) required to completely fill the tank?Solution
Pipe X fills in 8 hours → rate = 1/8 Pipe Y fills in 10 hours → rate = 1/10 Pipe Z empties in 15 hours → rate = 1/15 For the first 4 hours, only X and Y work:(1/8 + 1/10) × 4 = 9/40 × 4 = 36/40 = 9/10 So, 90% of the tank is filled. Now X, Y, and Z work together: (1/8 + 1/10 + 1/15) = 19/120 ​Remaining work = 1 − 9/10 = 1/10​ Time to finish = (1/10)/(19/120) = 12/19 hrs Total time = 4 + 12/19 = 88/19 hrs
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