acertijo del deposito 


The riddle of the water tank or the tank issue is one of the content in the book "The nine chapters on mathematical art" one of the oldest books math China, dating back to the period of Zhou Dynasty.

We have a water tank of 48 m3 capacity with two filling pipes and drain.
The first filler pipe open one would take 12 hours to fill the tank.
The second filler pipe open only take six hours to fill the tank.
With fully fueled and two filling lines closed, the discharge pipe would take eight hours to remove all the water and leave the empty tank.

If we start from the empty tank and open the three pipes how long it would take to fill the tank?

The first pipe fills reservoir 48 m3 within 12 hours, so its volume is 4 m3 / h
The second pipe fills reservoir in 6 hours, so its volume is 8 m3 / h
The two pipes together have a total flow of 12 m3 / h
The discharge pipe takes 8 hours to get 48 m3 so the drain flow is 6 m3 / h
If you enter 12 m3 / h and leaving 6 m3 / h what is left in the tank is 6 m3 / h
If they enter 6 m3 / h tank will be filled within 8 hours.