SOLUTION: If a hot-water faucet can fill a sink in 9 min. and a cold-water faucet can fill it in 6. Also, the drain is open which empties the sink in 25 min. How long will it take to fill th

Question 216001: If a hot-water faucet can fill a sink in 9 min. and a cold-water faucet can fill it in 6. Also, the drain is open which empties the sink in 25 min. How long will it take to fill the sink us...ing both faucets and the open drain???
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If a hot-water faucet can fill a sink in 9 min. and a cold-water faucet can fill it in 6. Also, the drain is open which empties the sink in 25 min. How long will it take to fill the sink us...ing both faucets and the open drain???
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This type of problem uses the inverses of the numbers given.
The hot water fills 1/9 of the tank per minute.
The cold water fills 1/6 per minute.
The drain empties 1/25 per minute.
The total is 1/9 + 1/6 - 1/25 tank/minute.
= (50 + 75 -3)/450 = 122/450 tank per minute.
The, it's 450/122 minutes per tank
= 225/61
= ~ 3.688 minutes
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As a check, the 2 faucets together with the drain closed would take (there's a shortcut with 2 elements, product/sum)
6*9/(6+9) = 54/15 = 3.6 minutes
Having the drain open adds time.
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