At a dairy plant, a milk tank can be filled in 6 hours (using the in-valve). Using the out-valve, the tank can be emptied in 15 hours. If both valves are open and milk is being pumped into the tank, how long will it take to fill the tank?

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Answer 1 · 2018-06-15T07:25:58

10 hours

the solution is independent of the volume (content) of the tank, but for better understanding, let's assume the tank contains A litres.

filling A litres in 6 hours means the filling speed is #Axx1/6 (litres)/(hour)#.

emptying A litres in 15 hours means the emptying speed is #Axx1/15 (litres)/(hour)#.

So the net speed, when both filling and emptying at the same time is:
# Axx (1/6-1/15) = Axx (5/30-2/30) = Axx(3/30) = Axx 1/10 (litres)/(hour)#

This means that our tank with A litres will be full in 10 hours

At a dairy​ plant, a milk tank can be filled in 6 hours​ (using the​ in-valve). Using the​ out-valve, the tank can be emptied in 15 hours. If both valves are open and milk is being pumped into the​ tank, how long will it take to fill the​ tank?