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A 12-gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and a drain
that lets water out at a rate of 1.5 gallons per minute. If you start with 3 gallons of water
in the tub, how long will it take to fill the tub completely?
3-in plus 1.5-out every minute means a net gain of 1.5 per minute. You need to fill (12 - 3) = 9 gallons. At 1.5 per minute, it takes 9/1.5 = 6 minutes if the drain and the faucet arr both open, but only (9/3)=3 minutes if you close the drain while you fill the tub.
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