Two hoses (X and Y) are filling a pool. Working alone at their individual constant rates, Hose X could fill the pool in 6 hours and Hose Y could do it in 4 hours. If the two hoses work together to fill half the pool, and then Hose Y finishes alone, how long will it take to fill the pool?

2 hours, 48 minutes
3 hours
3 hours, 12 minutes
3 hours, 24 minutes
3 hours, 48 minutes