Assume that the filling rate or the emptying rate for each pipe i
1. Question: Pipe A can fill the tank in 20 hours while Pipe B alone can fill it in 30 hours and Pipe C can empty the tank in 40 hours. If all the pipes are opened together, in how long will the tank be full?
Let the capacity of the tank be C liters
Fill rate of A, Fa = C/20 liters per hr
Fill rate of B, Fb = C/30 liters per hr
Fill rate of C, Fc = - C/40 liters per hr [Negative since this pipe is emptying the tank]
Let t be the time taken to fill the tank to maximum capacity.
2. Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2.5 hours to fill the tank. If the pump is turned off, how long will it take to empty the tank?
Fill rate of pipe, Fp = C/2 liters per hr
Let the fill rate of the leak be FL
2.5 x [Fp + FL] = C => FL = - C/10
With the pump turned off, it would take 10 hrs for the leak to empty the tank.
Note: The problems on Pipes and Cisterns are much alike those on Time and Work so it is easy to draw analogy from them and can be solved following similar procedure. Time taken to fill/empty a cistern is equivalent to time taken to do a work. Different pipes are equivalent to the different workers.
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Pipes and Cisterns
Pipes and Cisterns: Cistern meaning, Pipes and Cisterns Questions, Solved Problems