SOLUTION: My word Problem is this: A tank can be filled by one pump in 50 minutes and by another pump in 60 minutes. A third pump can drain the tank in 75 minutes. If all 3 pumps go into ope

Question 1053962: My word Problem is this: A tank can be filled by one pump in 50 minutes and by another pump in 60 minutes. A third pump can drain the tank in 75 minutes. If all 3 pumps go into operation, how long will it take to fill the tank?
I have made a table like this:
Pump | Minutes | In One Minute | In x minutes
P1 | 50 | 1/50 | 1/50x
P2 | 60 | 1/60 | 1/60x
P3 | 75 | 1/75 | 1/75x
this is my solving:
1/50x + 1/60x + 1/75x = 1
simplified:
6/300x + 5/300x + 4/300x = 1
My final answer was 25. When I checked online it said I was wrong. I would like to know where my mistake is.
Thanks for taking the time to help me!
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
Let n be the amount of time taken to fill the tank. If all 3 pumps are going at the same time, then:
n/50 + n/60 -n/75=1 (The third pump DRAINS the tank.)
So:
6n/300 + 5n/300 - 4n/300=1
7n=300
n=300/7
It will take 300/7 minutes to fill the tank. ☺☺☺☺

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