SOLUTION: If a vat of acid can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 20 hours, how long will it take to fill the vat if both pipes are open?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If a vat of acid can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 20 hours, how long will it take to fill the vat if both pipes are open?      Log On


   

Question 352105: If a vat of acid can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 20 hours, how long will it take to fill the vat if both pipes are open?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
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Let the vat volume equal Z.
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Fill rate: R%5Bf%5D%2A10=Z
R%5Bf%5D=Z%2F10
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Draining rate: R%5Bd%5D%2A18=Z
R%5Bd%5D=Z%2F18
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With both valves open,
%28R%5Bf%5D-R%5Bd%5D%29%2At=Z
Substitute from above,
%28Z%2F10-Z%2F18%29%2At=Z
%289%2F90%29Z-%285%2F90%29Z%29%2At=Z
%284%2F90%29Z%29%2At=Z
t=90%2F4
highlight%28t=22.5%29hrs