SOLUTION: One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How long will it take the pipe to fill the pool if the drain is left open?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How long will it take the pipe to fill the pool if the drain is left open?      Log On


   

Question 1131672: One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How long will it take the pipe to fill the pool if the drain is left open?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The usual way to work a problem like this is to think about the fraction of the "job" each "worker" does in 1 hour. In this problem, the input pipe FILLS 1/6 of the pool each hour and the drain EMPTIES 1/10 of the pool each hour.

So if the drain is left open when the pool is being filled, the fraction of the pool that is filled in 1 hour is 1/6 - 1/10 = 5/30-3/30 = 2/30 = 1/15.

So it will take 15 hours to fill the pool if the drain is left open.

Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Filling is taken (or could) as positive. Draining or emptying can then be taken as NEGATIVE filling.

Filling Rate using both pipes at the same time:
1%2F6-1%2F10

5%2F30-3%2F30

2%2F30

1%2F15

15 hours to fill