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Question 112134: One pump can fill a water tank in 25 minutes. Another pump can fill the same tank in 50 minutes. If the first pump is open for 5 minutes before the second is opened, how long will it take to fill the tank?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=the time it takes both pumps working together to fill the tank after the second pump is opened.
Now the first pump can fill at the rate of 1/25 tank per minute
The second pump can fill at the rate of 1/50 tank per min
Together they can fill at the rate of 1/50+1/25 =1/50+2/50=3/50 tank per minute
If we open the first pump for 5 min, then it fills (1/25)*5 or 1/5 of the tank leaving 4/5 of the tank to be filled by pump #1 and #2 working together
So our equation to solve is:
(3/50)x=4/5 multiply each term by 50
3x=40 divide both sides by 3
x=13.333333333 minutes ---------time to fill the tank after pump #2 is opened
Total time, of course, would be 13.333333333333+5 or 18.33333333333 min
CK
(3/50)(13.333333333)+(2/50)(5)=1 (one tank, that is)
40/50+10/50=1
1=1
Hope this helps---ptaylor
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