SOLUTION: An empty swimming pool can be filled in 10 hours. When full, the pool can be drained in 19 hours. How long will it take to fill the empty pool if the drain is left open?

Question 332663: An empty swimming pool can be filled in 10 hours. When full, the pool can be drained in 19 hours. How long will it take to fill the empty pool if the drain is left open?
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
Put things in terms of proportion of the pool emptied or filled per hour
--
Fiilled: 1/10 of the pool every hour
Emptied: -1/19 of the pool every hour (negative means its being drained)
--
filled if drain is open: both fill and drain at the same time (working together) = 1/10 - 1/19 every hour
--
So every hour 1/10 - 1/19 fill 1/x of the pool
1/10-1/19=1/x
get common denominator
--
19/190 - 10/190 = 1/x
9/190 = 1/x (solve for x)
x=190/9= 21+1/9 hours or apprx 21 hours and 7 minutes

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