SOLUTION: A swimming pool can be filled in 12 hours, and requires 18 hours to drain. If the drain was accidentally left open for 12 hours while the pool was being filled. How long did it tak

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A swimming pool can be filled in 12 hours, and requires 18 hours to drain. If the drain was accidentally left open for 12 hours while the pool was being filled. How long did it tak      Log On


   



Question 351547: A swimming pool can be filled in 12 hours, and requires 18 hours to drain. If the drain was accidentally left open for 12 hours while the pool was being filled. How long did it take to fill the pool?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
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Let Z be the volume of the pool.
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Filling rate: 12%2AR%5Bf%5D=Z
1. R%5Bf%5D=Z%2F12
Draining rate:18%2AR%5Bd%5D=Z
2. R%5Bd%5D=Z%2F18
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Filling while the drain is open for 12 hrs: %28R%5Bf%5D-R%5Bd%5D%29%2A12=Z1
Find Z1.
Substituting from eq. 1 and eq. 2,
%28Z%2F12-Z%2F18%29%2A6=Z1
Z1=Z%281%2F2-1%2F3%29=Z%2F6
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Z-Z%2F6=%285%2F6%29Z still needs to be added
Find that time, now the drain has been closed.
R%5Bf%5D%2At=%285%2F6%29Z
%28Z%2F12%29%2At=%285%2F6%29Z
+t=10+ hrs
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Total time:T=12%2B10
highlight%28T=22%29 hrs