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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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Math Expert

Joined: 02 Sep 2009

Posts: 58320

Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink]

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31 Jan 2019, 09:07

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Difficulty:

45% (medium)

Question Stats:

65% (01:38) correct

35% (01:32) wrong

based on 82 sessions

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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

Spoiler: OA

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Two pipes A and B can fill a tank in 8 hours. If only pipe A is open [#permalink]

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31 Jan 2019, 09:12

Bunuel wrote:

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]

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31 Jan 2019, 09:52

Bunuel wrote:

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]

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04 Feb 2019, 19:02

Bunuel wrote:

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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