Pipes
Pipes A and B fill water into a tank of capacity 1000 liters at the rate of 100 liter/minute and 25 lite/Minute respectively. Pipe C drains water from the same tank at the rate of 50 liters/minute. Pipe B is kept open for a minute and then closed, then the drain pipe C is kept open for a minute and then closed then pipe A is kept open for a minute and then closed. This process is repeated until the tank is full. How long will it take to fill the tank?(in minutes)
The answer is 39.
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1 solution
We can ignore the first two minutes as in the first minute, pipe B will add 25 litres to the tank, all of which will be drained out by pipe C during the second minute, so the tank will be empty again. After the first two minutes, the pipes will rotate in the order A, B, C, A, B, C,... so the sequence of gains or losses of water from the tank will be + 1 0 0 , + 2 5 , − 5 0 , + 1 0 0 , + 2 5 , − 5 0 , … so after every three minutes the tank has a net gain of 75 litres. Repeating this for twelve three-minute cycles, the tank will gain 1 2 × 7 5 = 9 0 0 litres, and when pipe A operates for another minute the tank will be full. Including the initial two minutes, the total time is 2 + 1 2 × 3 + 1 = 3 9 minutes.