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A water tank has two valves, one for inlet pipe and the other is outlet pipe. If the tank is empty the inlet valve is

opened, the tank will be full of water after 5 hours. If the tank is full and the outlet valved is opened, the tank

will be emptied in 8 hours. Suppose the tank is empty and both valves are opened, in how many hours will the

tank be full?

Respuesta :

LammettHash

Let V be the volume of the tank. The inlet pipe fills the tank at a rate of

V / (5 hours) = 0.2V / hour

and the outlet pipe drains it at a rate of

V / (8 hours) = 0.125V / hour

With both valves open, the net rate of water entering the tank is

(0.2V - 0.125V ) / hour = 0.075V / hour

If t is the time it takes for the tank to be full, then

(0.075V ) / hour • t = V

Solve for t :

t = V / ((0.075V ) / hour)

t = 1/0.075 hour

t ≈ 13.333 hours

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