A distillate flows into an empty 64-gallon drum at spout A and out of the drum at spout B

GRE Quant Problem Solving
1

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 out 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

Answer: D

I solved this by saying at its current rate, it will take 32 hours to fill this drum. But I want it to take 96 hours, so I’d like my speed to be 1/3 as fast.

So I want Unit B to “take away” 2/3 of the amount each time Unit A does one unit of work. 2-(2/3) = 4/3.

I got the correct answer but I am thinking algebra might be a better way to go about these questions. I watched Greg’s explanation on this but don’t understand how to approach doing algebra with two different rates. Can anyone clarify this process for me? Thanks

2

The approach in such questions where there is both inward and outward flow is to add and subtract the rates. Inward flow would get a positive sign whereas outward flow gets a negative sign.
W = R*T
64 = (2-x)*96
x=4/3

3

Wow, you made that convoluted problem look very simple. Thank you! :smile:

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