The time it takes to empty a full tank in case both the pipes are open is calculated to be 3 hours.
The time it takes to empty a full tank can be calculated by using an algebraic expression as follows;
Consider; x = time it takes to empty the full tank if both pipes are open
Then with both pipes open, the tank empties at the rate of (1/x) tank per minute
Inlet pipe fills at the rate of 1/90 tank per minute and outlet pipe empties at the rate of 1/60 tank per minute
So with both pipes open the tank empties at the rate = (1/60-1/90) tank per min
Therefore;
1/60 - 1/90 = 1/x
multiply each term by 180x
(1/60)(180x) - (1/90)(180x) = (1/x)(180x)
3x - 2x= 180
x = 180 min or 3 hr
Hence it takes 3 hours to empty the full tank.
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