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?

- - 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).

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