It takes 6 hours to fill a pool with the inlet pipe. It can be emptied in 12 hours with the outlet pipe. If the pool is 2/3 full to begin with, how long will it take to fill it from there if both pipes are open?

4 hours

Step-by-step explanation:

The least common multiple of 6 and 12 is 12. So let's assume the pool has a volume of 12 units.

The inlet pipe fills the pool at a rate of 12 units / 6 hours = 2 units per hour, and the outlet pipe drains the pool at a rate of 12 units / 12 hours = 1 unit per hour.

In total, water is added at a rate of 2 units/hr - 1 unit/hr = 1 unit/hr.

The pool is 2/3 full to begin with, so there's already 8 units of water in the pool, which leaves 4 units empty. At a rate of 1 unit/hr, it takes 4 hours to fill the pool.