Question
Two pipes can fill a cistern separately in 36 minutes
and 45 minutes, respectively. A waste pipe can drain off 40 litres per minute. If all the three pipes are opened, the cistern fills in one hour. The capacity (in litres of the cistern) is:Solution
Let's denote the capacity of the cistern as C liters. We then have: The rate of the first pipe is C/36 liters per minute. The rate of the second pipe is C/45 liters per minute. The waste pipe drains at a rate of 40 liters per minute. When all three pipes are open, the cistern is filled in 60 minutes (1 hour), meaning the net rate is C/60 liters per minute. (C/36) + (C/45) - 40 = C/60 5C + 4C-7200 = 3C 6C = 7200 C = 7200/6 = 1200 So, the capacity of the cistern is 1200 liters.
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