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 8 hours. How long will it take to fill the vat if

Algebra ->  Rate-of-work-word-problems -> 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 8 hours. How long will it take to fill the vat if      Log On


   

Question 473435: 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 8 hours. How long will it take to fill the vat if both pipes are left open?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 8 hours.
How long will it take to fill the vat if both pipes are left open?
:
let t = time required to fill the vat with both valves open
let the completed job = 1, (a full vat)
:
Fill is plus, empty is minus
:
t%2F3 - t%2F8 = 1
multiply by 24 to clear the denominators, result:
8t - 3t = 24
5t = 24
t = 24%2F5
t = 4.8 hrs to fill it with both valves open
:
:
Check
4.8/3 - 4.8/8 =
1.6 - .6 = 1; confirms our solution of t = 4.8