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Time taken to fill the drum

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Time taken to fill the drum

by gmattesttaker2 » Wed Feb 19, 2014 7:00 pm
Hello,

Can you please help with this problem:

A distillate flows into an empty 64-gallon drum at spout A and out of the drum at spout B. If the rate of flow through A is 2 gallons per hour, how many gallons per hour must flow at spout B so that the drum is full in exactly 96 hours?


A) 3/8
B) 1/2
C) 2/3
D) 4/3
E) 8/3

OA: D

Thanks,
Sri
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by Brent@GMATPrepNow » Wed Feb 19, 2014 7:31 pm
gmattesttaker2 wrote: A distillate flows into an empty 64-gallon drum at spout A and out of the drum at spout B. If the rate of flow through A is 2 gallons per hour, how many gallons per hour must flow at spout B so that the drum is full in exactly 96 hours?

A) 3/8
B) 1/2
C) 2/3
D) 4/3
E) 8/3
We want to fill 64-gallon drum in 96 hours.
rate = amount/time
So, rate = 64 gallons/96 hours = 2/3 gallons per hour
So, we want water to flow into the drum at a NET RATE of 2/3 gallons per hour so that the drum will fill in 96 hours.

NET rate: (rate of water flowing into drum) - (rate of water flowing out of drum)
2/3 = 2 gallons per hour - (rate of water flowing out of drum)
So, (rate of water flowing out of drum) = 2 - 2/3 = [spoiler]4/3[/spoiler]

Answer: D

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Brent
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by [email protected] » Thu Feb 20, 2014 1:20 am
Hi Sri,

The answer choices to this question are "spread out" in such a way that there's a fast way to solve this problem without doing too much math...

The "intake" flows in at 2 gallons/hour, but the "outtake" flows enough that a 64 gallon tank takes 96 hours to fill up.

If the outtake was 1 gallon/hour, then the "net" fill-up would be 1 gallon/hour and would take 64 hours to fill the tank. Since the tank takes LONGER to fill up, that means the outtake was GREATER than 1. Eliminate A, B and C.

Answer E is 8/3 which is MORE than the intake of 2 gallons/hour. Under these circumstances, the tank would NEVER fill up. Eliminate E.

Final Answer: D

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Rich
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