SOLUTION: Filling a hot tub with a hose takes 4 hours. Draining the same tub takes 7 hours. If the drain is open, how long will it take to fill the tub?

Question 828690: Filling a hot tub with a hose takes 4 hours. Draining the same tub takes 7 hours. If the drain is open, how long will it take to fill the tub?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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hose rate:
r = v/t = 1/4
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drain rate:
r = v/t = 1/7
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net rate:
1/4 - 1/7
7/28 - 4/28
3/28
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time = 1/rate
net time to fill the tub with hose and drain open = 28/3 = 9.333333 = 9 hours and 20 minutes
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