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?

Question

3800 views around the world

You can reuse this answer
Creative Commons License

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?