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Question 77449: A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes to empty full tank if both pipes are accidentally left open
Inlet pipe fills at the rate of 1/45th tank per minute
Drain pipe empties at the rate of 1/30th tank per minute
If both are open, tank empties at the rate of 1/30-1/45 tank per minute
1/30-1/45 --- LCM is 90
1/30=3/90
1/45=2/90
So:
If both are open, tank empties at the rate of 3/90-2/90=1/90th tank per minute
Now the question is: If the tank is full (90/90 cu units) when both pipes are accidentally left open, how long will it take to empty the tank? So our equation to solve is:
(1/90)x=90/90 multiply both sides by 90
x=90 minutes-------------------------------ans
CK
Number of minutes times empty rate-number of minutes times fill rate =1(full tank emptied)
90(1/30)-90(1/45)=1
3-2=1
1=1
Hope this helps---ptaylor
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