SOLUTION: A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 5 hours. How long will it take to fill the vat

Question 402276: A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 5 hours. How long will it take to fill the vat if both pipes are left open?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes to fill the vat with both pipes open
Then, with both pipes open, the vat fills at the rate of 1/x vat per hr
The inlet pipe fills at the rate of 1/3 vat per hour
The outlet pipe empties at the rate of 1/5 vat per hour
So, with both pipes open the vat fills at the rate of 1/3 - 1/5 =2/15 vat per hour
Now our equation to solve is:
2/15 = 1/x multiply each side by 15x
2x=15
x=7.5 hours time it takes to fill the vat with both pipes open
CK
In 7.5 hours, the inlet pipe fills (1/3)*7.5=2.5 vats
In 7.5 hours the outlet pipe empties (1/5)*7.5=1.5 vats
So, 2.5-1.5=1 vat
Hope this helps---ptaylor
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