Respuesta :
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
[tex] A = 1/4 -B [/tex]
[tex]A = (1 - 4B)/4 [/tex] ....4
sub equation 4 into 2
[tex](1 - 4B)/4 + C = 1/5 [/tex]
[tex]C = B - (1/20)[/tex]
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
Answer: T = 3 hours 14.6minutes
Step-by-step 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
