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 8 hours. If both valves are open and milk is being pumped into the tank, how long will it take to fill the tank?
1 Answer
Nov 19, 2017
It takes 24 hours to fill. Work this out on the basis of the rate of filling per hour. Details below...
Explanation:
Since it takes 6 hours to fill the tank, in each one hour, the tank is filled to 1/6 of its capacity.
Likewise, since it takes 8 hours to empty the tank, each one hour, the tank loses 1/8 of its capacity.
So, the total change per hour is
That is, the tank is 1/24 closer to full after each hour. Therefore it takes 24 hours to fill the tank.