A pool has two pipes, one that pours water into the pool, and one that drains water from the pool. It takes $6\text{ hours}$ for a pipe to fill an empty pool with the other pipe closed. It takes $9\text{ hours}$ for a pipe to empty this pool when full (also with the other pipe closed).

If the pool is empty and both pipes are turned on at the same time, how long will it take for the pool to fill?