SOLUTION: One pump can empty the town swimming pool in 7h less time than a second pump can. Together they empty the pool in 12h. How long would it take the larger pump alone to empty it.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One pump can empty the town swimming pool in 7h less time than a second pump can. Together they empty the pool in 12h. How long would it take the larger pump alone to empty it.       Log On


   

Question 747741: One pump can empty the town swimming pool in 7h less time than a second pump can. Together they empty the pool in 12h. How long would it take the larger pump alone to empty it.
I have tried setting up an equation involving the two pumps (x+7) and x, however I can't see how I should relate them to total time it takes to fill the pool?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x = the time in hours for second pump to empty the pool.
"Emptying the pool" is one job.

One Pump rate is 1%2F%28x-7%29
Second Pump rate is 1%2Fx
One Pump AND Second Pump at same time, rate is 1%2F12

The rates are additive using ordinary arithmetical addition.
highlight%281%2F%28x-7%29%2B1%2Fx=1%2F12%29.
Simplest common denominator is 12x%28x-7%29, so multiply both sides of the equation by 12x%28x-7%29 to clear the denominators. Continue solving for x.