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?

Total time to fill pool is 3 hours 12 minutes

Step-by-step explanation:

Time taken for hose X to fill alone = 6 hours

Time taken for hose y to fill alone = 4 hours

Let the capacity of the pool = A

Ø Work rate when X works alone = A/6

Ø Work rate when Y works alone = A/4

Combined workrate when hoses X & Y work in conjunction will be

A/6 + A/4 = (4A + 6A) / 24 = 10A/24

Therefore, combined rate = 5A/12

Notice that workrate = capacity/time

Ø Time = capacity/workrate

Time taken when both hoses work = capacity / combined workrate = A / (5A/12) = A * (12/5A) = 12/5

Time taken is 2.4 hours = 2 hours 24 minutes

Since both hoses work together to half the pool

Time taken to fill half the pool = 2 hours 24 minutes/2 = 1 hour 12 minutes

The remaining half is filled by Y alone

Total time to fill pool is 1 hour 12 minutes plus 4/2 hours (Y is filling up half the pool by itself) = 3 hours 12 minutes