Aswimming pool can be filled by any of three hoses a, b or c. hoses a and b together take 4 hours to fill the pool. hoses a and c together take 5 hours to fill the pool. hoses b and c together take 6 hours to fill the pool. how many hours does it take hoses a, b and c working together to fill the pool?

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

i need a picture

step-by-step explanation: