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GRE Math Challenge #26-Pump A can empty a pool in 8 minutes
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06 Nov 2015, 19:26
06 Nov 2015, 19:26
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Question Stats:
54% (01:56) correct
45% (02:01) wrong based on 31 sessions
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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?
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Show: :: OA
\(\frac{32}{7}\)
Re: GRE Math Challenge #26-Pump A can empty a pool in 8 minutes
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06 Jan 2016, 10:34
06 Jan 2016, 10:34
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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
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
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24 Aug 2016, 05:56
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
Answer:
Show: ::
32/7
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