Question

It takes 10min to fill an empty tub. It takes 12 to drain a full tub. How long will it take to fill the tub with the plug out?

Answer 1

After 12 minutes: 
Tub is "2 minutes" full
After 24 minutes:
Tub is "4 minutes" full.
After 36 minutes: 
Tub is "6 minutes" full
After 48 minutes:
Tub is "8 minutes" full.
After 60 minutes:
Tub is 10 minutes full, or just full
60 minutes

Answer 2

-- Water pouring into a tub with the drain closed
fills 1/10 of the tub each minute.

-- Water draining from a tub with the faucets off
empties 1/12 of the tub each minute.

When the faucet is filling AND the drain is draining, the tub collects

         (1/10) - (1/12) of a tub each minute.

         (1/10) - (1/12) = (6/60 - 5/60) = 1/60 of a tub per minute.

 Filling (1/60) (tub/minute) corresponds to the unit rate of (60/1) (minute/tub).