SOLUTION: A swimming pool is being drained through the drain at the bottom of the pool, and filled by a hose at the top. If the hose can fill the pool in 21 hours and the drain can empty the

Question 538098: A swimming pool is being drained through the drain at the bottom of the pool, and filled by a hose at the top. If the hose can fill the pool in 21 hours and the drain can empty the pool in 24 hours, how many hours would it take to fill the tank if the drain were left open?

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Hose can fill the pool in 21 hours, so it does 1/21 of the job per hr.
Drain can empty the pool in 24 hours, so it does 1/24 of the job per hr.
.
(1/21 - 1/24)*x hr = 1 whole job
.
((24-21)/(21*24))*x = 1
(3/504)*x = 1
3x = 504
x = 168
.
Answer: With the hose filling the pool and the drain emptying the pool simultaneously, it will take 168 hr to fill the pool.
.
Check the answer
168/21 - 168/24 = ?
8 - 7 = 1
Correct.
.
Done.
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