A 12 gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and has a drain that lets water out at a rate of 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?

Tub's total capacity = 12 gallon. Question dictates Tub has 3 gallons already filled up. So we have to find out what time it takes to fill up rest 9 gallon (12-3) considering the faucet and drain.

As given for faucet, it takes 1 min to fill up 3 gallons

and it takes 1 min to drain 1.5 gallons.

So within 1 min the tub actually fills 1.5 gallons (3-1.5)

Now 1.5 gallons are filled up in 1 min

         1 gallon is filled up in 1/1.5 min

 so    9 gallons are filled up in (1/1.5) *9 mins = 6 mins (ANS)