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
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X alone 6h = work rate 1/6
Y alone 4h= work rate 1/4
X+Y together= 1/6+1/4= 4/24+6/24=10/24=5/12 --> so 15/2h for Pool (work rate* Time= Unit --> 5/12* X = 1 pool --> X(hours)=12/5=2h 24 min (Note: 12/5=2 2/5 --> 2 12*2/60 --> 2h 24/60 h --> 2h 24 min

Since X+Y only fill half of the pool together they take 1h 12 min for the first half.
Then, Y fills the remaining amount on his own. This takes him 2h (since he needs 4h for the complete pool)

Finally the total time is : XY working together time + Y alone time = 1h 12min + 2h = 3h 12min