SOLUTION: A swimming pool can be filled in 6 hours and requires 9 hours to drain. If the drain was accidentally left open for 6 hours while the pool was being filled, how long did filling th

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Question 357840: A swimming pool can be filled in 6 hours and requires 9 hours to drain. If the drain was accidentally left open for 6 hours while the pool was being filled, how long did filling the pool require?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
Let the pool volume be V.
Find the filling rate.
R%5Bf%5D%2A6=V
R%5Bf%5D=V%2F6
Find the draining rate.
R%5Bd%5D%2A9=V
R%5Bd%5D=V%2F9
Find the volume in the pool for 6 hours with both valves open.
%28R%5Bf%5D-R%5Bd%5D%29%2A6=%28V%2F6-V%2F9%29%2A6
%28R%5Bf%5D-R%5Bd%5D%29%2A6=%28%283V%29%2F18-%282V%29%2F18%29%2A6
%28R%5Bf%5D-R%5Bd%5D%29%2A6=%28V%2F18%29%2A6
%28R%5Bf%5D-R%5Bd%5D%29%2A6=V%2F3
The pool is now (1%2F3) full.
Find the time it takes to fill the remaining %282%2F3%29V.
R%5Bf%5D%2At=%282%2F3%29V
%28V%2F6%29%2At=%282%2F3%29V
t=4hrs.
The total time to fill the pool is the sum of the two times.
T=6%2B4
highlight%28T=10%29hrs