Since there are 24 hours in one day,

in one hour first tap fills 1/48,

the second tap 1/72,

the third tap 1/96 and

the fourth tap fills 1/6 of the Pool.

That is all together (6+4+3+48) / 288 = 61/288.

The Pool will be full in 288/61 hours,

which is 4 hours 43 minutes and about 17 seconds.