SOLUTION: A swimming pool can be filled in 15 hours if water enters through a pipe alone. 23 hours if water enters through a hose alone. How long will it take to fill the pool if water is en

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Question 666302: A swimming pool can be filled in 15 hours if water enters through a pipe alone. 23 hours if water enters through a hose alone. How long will it take to fill the pool if water is entering through both the pipe and the hose?
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
We start by turning the times into rates.

A pipe can fill the swimming pool in 15 hours, so the rate for the pipe is 1%2F15 of a swimming pool per hour.

A hose can fill the swimming pool in 23 hours, so the rate for the hose is 1%2F23 of a swimming pool per hour.

Their combined rate, r, is 1%2F15+%2B+1%2F23 of a swimming pool per hour.
r+=+1%2F15+%2B+1%2F23
r+=+%2823%2F23%29%281%2F15%29+%2B+%2815%2F15%29%281%2F23%29
r+=+23%2F345+%2B+15%2F345
r+=+%2823+%2B+15%29%2F345
r+=+38%2F345 of a swimming pool per hour

So both the pipe and the hose together will take 345%2F38+=+9%263%2F38 hours to fill the pool, or 9 hours 4 minutes and 44.21 seconds.