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You are here: Experts > Science > Math for Kids > Word Problems > Math
Expert: Soroban
Date: 2/12/2008
Subject: Math
Question
Suppose that a large pump can empty a swimming pool in 50 hrs and that a small pump can empty the swimming pool in 80hrs. How long does it take to empty the pool if both pumps are used? Show work.
Answer
Hello, Angela!
I have a favorite approach to these "Work" problems.
I hope you like it.
Pump A takes 50 hours to do the job.
In one hour, it does 1/50 of the job.
In x hours, it does x/50 of the job.
Pump B takes 80 hours to do the job.
In one hour, it does 1/80 of the job.
In x hours, it does x/80 of the job.
Working together for x hours, they can do: x/50 + x/80 of the job.
But in x hours, we expect them to do the entire job (1 job).
There is our equation . . . x/50 + x/80 = 1
Multiply by 400: 8x + 5x = 400
and we have: 13x = 400 --> x = 400/13
Therefore, it takes 400/13 hours (roughly 30 hours, 46 minutes)
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