A vessel has three pipes connected to it, two to supply liquid and one to draw liquid. The first and second pipe can fill the vessel in 9/2 and 3 hours and the third can empty it in 3/2 hours. If all the pipes are one simultaneously when the vessel is half full, how soon will it be emptied?

Question: A vessel has three pipes connected to it, two to supply liquid and one to draw liquid. The first and second pipe can fill the vessel in 9/2 and 3 hours and the third can empty it in 3/2 hours. If all the pipes are one simultaneously when the vessel is half full, how soon will it be emptied?

Solution:
in one hour the tank will be emptied = 2/3 - 2/9 - 1/3
= 1/9

∴ the vessel will be emptied in = 9/2 = 4.5 hours