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GRE Math Challenge #26-Pump A can empty a pool in 8 minutes

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GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  06 Nov 2015, 19:26
Expert's post
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Question Stats:

100% (03:18) correct 0% (00:00) wrong based on 2 sessions
Pump A can empty a pool in 8 minutes.Pump B can empty a pool in 6 minutes.Pump A pumps the pool for 2 minutes before pump B joins in.How may minutes will it take to empty the pool together?

[Reveal] Spoiler: OA
$$\frac{32}{7}$$

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Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  06 Jan 2016, 10:34
Pump A working alone for 2 minutes pumped 1/4 pool. 3/4 pool is remained for pumping together.

pump A pumps 3 pools in 24min
pump B pumps 4 pools in 24min
so 7 pumps in 24min together >> one pool 24/7 min.

total time of pumping= 2min+ 3/4*24/7 = 4.57 min
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Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  24 Aug 2016, 05:56
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sandy wrote:
Pump A can empty a pool in 8 minutes.Pump B can empty a pool in 6 minutes.Pump A pumps the pool for 2 minutes before pump B joins in.How may minutes will it take to empty the pool together?

Let's assign a nice value for the volume of the pool and go from there.

Pump A can empty a pool in 8 minutes.Pump B can empty a pool in 6 minutes.
The least common multiple of 8 and 6 is 24.
So, let's say that the TOTAL volume of the pool is 24 gallons.

If pump A can empty a pool in 8 minutes, then pump A's rate = 24 gallons/8 minutes = 3 gallons per minute
If pump B can empty a pool in 6 minutes, then pump B's rate = 24 gallons/6 minutes = 4 gallons per minute
So, there COMBINED rate = 3 + 4 = 7 gallons per minute

Pump A pumps the pool for 2 minutes before pump B joins in.How may minutes will it take to empty the pool together?
First 2 minutes: At a rate of 3 gallons per minute, pump A removes 6 gallons from the pool, which means the amount REMAINING in the pool = 24 - 6 = 18 gallons

At a COMBINED rate of 7 gallons per minute, the time it takes to remove the remaining 18 gallons = 18/7 minutes

So, the TOTAL TIME it takes to empty the pool = 2 minutes (pump A alone) + 18/7 minutes (together) = 32/7 minutes

[Reveal] Spoiler:
32/7

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Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  28 Jul 2017, 03:12
Hi Brent,
I did the same calculations that you did, but at the end of the problem I subtracted 2 minutes from 4.57 minutes because during those two minutes the machines were not working together. I was confused by the wording of the question since it asked for the time it took for the machines to empty the pool together, so I thought the answer would be 2.57 minutes. Will the questions on the GRE be phrased like this as well?
Amy
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Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  28 Jul 2017, 05:16
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Expert's post
AmyK wrote:
Hi Brent,
I did the same calculations that you did, but at the end of the problem I subtracted 2 minutes from 4.57 minutes because during those two minutes the machines were not working together. I was confused by the wording of the question since it asked for the time it took for the machines to empty the pool together, so I thought the answer would be 2.57 minutes. Will the questions on the GRE be phrased like this as well?
Amy

I have a feeling, the test-makers would add some extra information to prevent ambiguity.
Perhaps something like...

Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. At 1:00pm Pump A starts pumping the pool. At 1:02pm, pump B joins in. At what time with the pool be empty?
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Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes [#permalink]  25 Dec 2017, 05:30
sandy wrote:
Pump A can empty a pool in 8 minutes.Pump B can empty a pool in 6 minutes.Pump A pumps the pool for 2 minutes before pump B joins in.How may minutes will it take to empty the pool together?

can you check the answer, since the stem says empty the pool together, I thought the answer is 18/7?
Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes   [#permalink] 25 Dec 2017, 05:30
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GRE Math Challenge #26-Pump A can empty a pool in 8 minutes

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