Answer:
3 hours 28 minutes
Step-by-step explanation:
Let A = the RATE at which hose A can fill the pool alone
Let B = the RATE at which hose B can fill the pool alone
Let C = the RATE at which hose C can fill the pool alone
Hoses A and B working simultaneously can pump the pool full of water in 4 hours
From Question. The combined RATE of hoses A and B is 1/4 of the pool PER HOUR
In other words, A + B = ¼
Hoses B and C working simultaneously can pump the pool full of water in 6 hours
From Question. The combined RATE of hoses A and C is 1/4 of the pool PER HOUR
In other words, B + C = 1/6
Hoses A and C working simultaneously can pump the pool full of water in 5 hours
From Question. The combined RATE of hoses A and C is 1/5 of the pool PER HOUR
In other words, A + C = 1/5
At this point, we have the following system:
A + B = 1/4 ...1
B + C = 1/6 ...2
A + C = 1/5 ...3
Considering equation one
....4
sub equation 4 into 2
Considering equation 3
B + [B-(1/20)] = 1/6
B =7/80
Sub B Into enq 1 and 2
A =13/80
C = 3/80
A+B+C = 23/80
3.47
=> 3 hours
0.47 × 60 = 28minutes