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?

A. 2 hours, 48 minutes
B. 3 hours
C. 3 hours, 12 minutes
D. 3 hours, 24 minutes
E. 3 hours, 48 minutes

[spoiler]OA=C[/spoiler]

Source: Veritas Prep