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?

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Answer 1 · 2017-11-19T00:43:49

It takes 24 hours to fill. Work this out on the basis of the rate of filling per hour. Details below...

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

#1/6-1/8 = 4/24 - 3/24 = 1/24#

That is, the tank is 1/24 closer to full after each hour. Therefore it takes 24 hours to fill the tank.

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?