Question

A swimming 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?

Answer 1

Answer: T = 3 hours 14.6minutes

Explanation:

Let A represent the fraction of the pool hose A alone can fill in one hour.

Let B represent the fraction of the pool hose B alone can fill in one hour.

Let C represent the fraction of the pool hose C alone can fill in one hour.

So, From the question;

Hose A and B fills 1/4 of the pool in one hour

Hose A and C fills 1/5 of the pool in one hour

Hose B and C fills 1/6 of the pool in one hour

Which gives the equation below

A + B = 1/4 ...1

B + C = 1/6 ...2

A + C = 1/5 ...3

Considering eqn 1

A = 1/4 -B

A = (1 - 4B)/4 ....4

substituting equation 4 into 2

(1 - 4B)/4 + C = 1/5

C = B - 1/20. .....5

Substituting equation 5 into 3

B + [B-1/20] = 1/6

2B = 1/6 + 1/20 = 13/60

B =13/120

Substituting B= 13/120 Into enq 5

C = 13/120 - 1/20 = 7/120

Substituting B into eqn 4

A = 1/4 - 13/120 = 17/120

When the three pumps are working simultaneously the fraction filled in one hour is

A+B+C = 37/120

The time taken to completely fill the pool is

T = 120/37 hours

T = 3.243243243243hours

T = 194.6minutes

T = 3 hours 14.6 minutes

Answer 2

3 hours 28 minutes

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

`A  = 1/4 -B`

`A = (1 - 4B)/4` ....4

sub equation 4 into 2

`(1 - 4B)/4 + C = 1/5`

`C = B - (1/20)`

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