SOLUTION: Could you help me with this work problem? I keep getting a negative result...is that correct? Question: An inlet pipe can fill a barrel with wine in 8 hrs, while an outlet pipe

Question 37597: Could you help me with this work problem?
I keep getting a negative result...is that correct?
Question:
An inlet pipe can fill a barrel with wine in 8 hrs, while an outlet pipe can empty it in 6 hrs. Through an error, both pipes on a full barrel are left open. How many hours will it take to empty the barrel?
This is what I have...
_________________________________________________
Rate Time to empty job done
_________________________________________________
inlet 1/8 x x/8
_________________________________________________
outlet 1/6 x x/6
_________________________________________________
x/8 - x/6 = 1
(find LCD) 24
(24)(x/8 - x/6) = (24)1
3x - 4x = 24
-x + 24
x = -24 hrs?
I need help!!!

Found 2 solutions by mszlmb, jorel1380:
Answer by mszlmb(115) (Show Source): You can put this solution on YOUR website!
ok 6hrs to empty 8hrs to fill
in 1hr, 1/6 is emptied and 1/8 filled
1-x/6+x/8=0
1 is the whole thing, x=hours
x/8-x/6=-1
3x/24-4x/24=-1
-x/24=-1
x/24=1
x=24

wat u did wrong is u frgot the 1st variable, 1. u wrote x/8-x/6=1, but it equals -1, IM me if u don't get sum of it.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
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.
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