Question 37597
To be honest, this problem, as phrased cannot be solved.  If both pipes are left open, the keg is draining faster than it can be filled, so it will never be full!!! It is emptying at 1/6th a keg per hour while it is filling at 1/8th a keg per hour.  Since 1/6th is greater than 1/8th, it will never be full.  

Maybe the question was meant to be phrased: filling at 1/6th a keg per hour and draining at 1/8th an hour...in which case the solution would be: t/6 - t/8=1 whole keg.  Solving for t we get 4t - 3t=24; thus t=24 hours it would take to fill the keg.