SOLUTION: A hose takes 15 minutes to fill a swimming pool and the drain empties the pool in 20 minutes. How long will it take to fill the pool if the drain is left open? I thought my teac

Question 682497: A hose takes 15 minutes to fill a swimming pool and the drain empties the pool in 20 minutes. How long will it take to fill the pool if the drain is left open?
I thought my teacher said the answer was 80 minutes but I only could figure out 1/15-1/20=1/60 making it 60 minutes. Can you explain my mistake please?
Found 2 solutions by josmiceli, rapaljer:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Add the rate of filling and subtract the rate of draining
Rate of filling = ( 1 pool filled ) / ( 15 min to fill )
Rate of draining = ( 1 pool drained ) / ( 20 min to drain )
Let = time in minutes to fill the pool

Multiply both sides by

It takes 1 hour to fill the pool with drain open
I think you are right, as long as the data is right.

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I'm sorry but I can't see how it could be 80 minutes, and I don't see anything wrong with your equation.

Let x = time it takes for the pool to fill given that the drain is open and the hose is turned on.

1/15 = amount of the pool filled in 1 minute with hose only and drain closed.
1/20 = amount of the pool emptied in 1 minute with the drain open and no hose.

, solve for x. The LCD is 60x, and the answer is x=60.

Why don't you re-post the problem. Maybe someone else has another idea on this one.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

P.S. Check out my website for full color explanations and lots of practice tests with detailed solutions for all levels of math at www.mathinlivingcolor.com.
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