Question

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?

Answer 1

10 hours

Explanation:

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