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Two pipes A and B can fill a tank in 8 hours. If only pipe A is open
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Bunuel
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Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink] New post  31 Jan 2019, 08:07
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Two pipes A and B can fill a tank in 8 hours. If only pipe A is open then it would take 4 hours longer to fill the tank. Find how much longer would it take if only pipe B is open.

A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 16 hours
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Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink] New post  31 Jan 2019, 08:12
Bunuel wrote:
Two pipes A and B can fill a tank in 8 hours. If only pipe A is open then it would take 4 hours longer to fill the tank. Find how much longer would it take if only pipe B is open.

A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 16 hours


given
AB/A+B = 1/8

time of A = 4 + 8 ; 12 hours
so
12B/12+B= 1/8
solve
B = 24 hours
so B would take 24-8 = 16 hours longer
IMO E
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Re: Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink] New post  31 Jan 2019, 08:52
Bunuel wrote:
Two pipes A and B can fill a tank in 8 hours. If only pipe A is open then it would take 4 hours longer to fill the tank. Find how much longer would it take if only pipe B is open.

A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 16 hours



solution:

rate of A+rate of B= total rate, and if the work done is one then we get the total time to finish.

1/A+1/B=1/Total

1/A+1/B=1/8. and given that rate of A=8+4=12 hours

so 1/12+1/B=1/8

1/B=1/8-1/12.. we get B as 24, now, how much longer tha 8 will it take then 24-8=16.

Option E.16 hours more
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Re: Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink] New post  04 Feb 2019, 18:02
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Bunuel wrote:
Two pipes A and B can fill a tank in 8 hours. If only pipe A is open then it would take 4 hours longer to fill the tank. Find how much longer would it take if only pipe B is open.

A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 16 hours


Let’s let B = the number of hours it takes pipe B to fill the tank. We see that the combined rate of A and B is 1/8, and since pipe A can fill the tank in 8 + 4 = 12 hours, the rate of pipe A is 1/12 and the rate of pipe B is 1/B; thus:

1/12 + 1/B = 1/8

Multiplying by 24B, we have:

2B + 24 = 3B

B = 24

So it would take 24 - 8 = 16 hours longer if only B is open.

Answer: E
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Re: Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink] New post  06 Jan 2021, 07:45
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Bunuel wrote:
Two pipes A and B can fill a tank in 8 hours. If only pipe A is open then it would take 4 hours longer to fill the tank. Find how much longer would it take if only pipe B is open.

A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 16 hours


Rate of \(A+B=\frac{1}{8}\)

Rate of \(A=\frac{1}{12}\) [4 hours more than the time both of them take together]

Rate \(B=\frac{1}{8}-\frac{1}{12}=\frac{1}{24}\)

So, B will take 24 hours to fill the tank alone, the time is \(24-8=16\) hours more than of both.

The answer is E,
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