SOLUTION: An 8 hp pump can fill a tank in 8 hours. A smaller 3 hp pump fills the same tank in 12 hours. The pumps are used together to begin filling this tank. After four hours, the 8 hp pum

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An 8 hp pump can fill a tank in 8 hours. A smaller 3 hp pump fills the same tank in 12 hours. The pumps are used together to begin filling this tank. After four hours, the 8 hp pum      Log On


   

Question 263393: An 8 hp pump can fill a tank in 8 hours. A smaller 3 hp pump fills the same tank in 12 hours. The pumps are used together to begin filling this tank. After four hours, the 8 hp pump breaks down. How long will it take the smaller pump to fill the tank?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is a working together problem.
The rate of the 8 hp pump = 1/8
the rate of the 3 hp pump is 1/12
The time together will be 4 hours.
The time that the 3 hp pump works alone is x hrs.
We want to fill only 1 tank
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we use the formula
%281%2F8%29%2A4+%2B+%281%2F12%29%2A4+%2B+%281%2F12%29%2Ax+=+1
we get
4%2F8+%2B+4%2F12+%2B+x%2F12+=+1
adding the fractions, we get
+5%2F6+%2B+x%2F12+=+1
subtract 5/6 to get
x%2F12+=+1%2F6
multiply by 12 to get
x+=+2
So, the 3 hp pump must work and additional 2 hours.