SOLUTION: Pump A can fill a swimming pool in 30 hours, while working together with pump B they will fill the pool in 12 hours. How much time would it take pump B to fill the pool?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pump A can fill a swimming pool in 30 hours, while working together with pump B they will fill the pool in 12 hours. How much time would it take pump B to fill the pool?      Log On


   

Question 713049: Pump A can fill a swimming pool in 30 hours, while working together with pump B they will fill the pool in 12 hours. How much time would it take pump B to fill the pool?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One job is filling the pool. Rate as gallons per hours.
Rate*Time=Jobs

Pump__________rate__________time_____________jobs
A_____________1/30_____________30____________1
B______________r______________(t)____________1
A & B__________1/12______________12_____________1

While A and B work together, each pump contributes its own rate to the sum of the simultaneous rates.

highlight%281%2F30%2Br=1%2F12%29, find r, which is units of jobs per hour. Note that the question is asking how many hours to fill the pool by pump B alone, which means how many hours per 1 job. This is the RECIPROCAL of r. We essentially are looking for t in the above table.

r=1%2F12-1%2F30
r=%285-2%29%2F30
r=3%2F30, highlight%28r=1%2F10%29
Answer: That means 10 hours for pump B to fill the pool