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

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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26 Aug 2018, 21:41
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35% (medium)

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70% (02:02) correct 30% (02:19) wrong based on 66 sessions

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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) $$\frac{3}{8}$$

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{4}{3}$$

(E) $$\frac{8}{3}$$

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Re: A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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26 Aug 2018, 22:15

Bunuel 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 out at spout B so that the drum is full in exactly 96 hours?

(A) $$\frac{3}{8}$$

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{4}{3}$$

(E) $$\frac{8}{3}$$

Rate of inlet flow at spout A=2gallons/hr
Resultant rate of water flow=$$\frac{64 gallon}{96 hours}=\frac{2}{3}$$gallons per hour

We have , rate of water inflow-Rate of water outflow=Resultant rate of water flow
Or, 2-Rate of water outflow=$$\frac{2}{3}$$
Or, Rate of water outflow=2-$$\frac{2}{3}$$=$$\frac{4}{3}$$

Ans. (D)
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Joined: 20 Feb 2017
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Re: A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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26 Aug 2018, 22:25
the rate of A =2
let the rate of B = x
the drum is full in exactly 96 hours, hence the capacity = 96*(2-x)
therefore,
96*(2-x) =64
or x= 4/3
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Re: A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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15 Sep 2019, 10:40
-- Without outlet B, drum would fill in 32 hrs (@2 gallons/hr rate).
-- If outlet rate (B) were 1 gallon/hr, then drum would take 64 hrs to fill (net rate is 1 gallon/hr) [+2inlet -1outlet]
-- Now, we know that it takes 96 hrs to fill! Clearly, the outlet is greater than 1 gallon/hr.
-- Look at options. A,B, and C are eliminated immediately.
-- Option E translates to 2.something. This is impossible. Drum would never fill in this case!
-- Pick D and move on.

Hope that helps
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Re: A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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15 Sep 2019, 12:37
Bunuel 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 out at spout B so that the drum is full in exactly 96 hours?

(A) $$\frac{3}{8}$$

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{4}{3}$$

(E) $$\frac{8}{3}$$

We would like the total flow in amount to be 64 gallons in 96 hours. That is saying we want the rate of flow in at 2/3 gal per hour. “A” flows in 2 gal/hour, which is too much.We want B to flow out the difference which is (2 - 2/3) = 4/3 gal/hour. Therefore we choose D.
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A distillate flows into an empty 64-gallon drum at spout A and out of  [#permalink]

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09 Oct 2019, 11:46
Bunuel 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 out at spout B so that the drum is full in exactly 96 hours?

(A) $$\frac{3}{8}$$

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{4}{3}$$

(E) $$\frac{8}{3}$$

We would like the total to be 64 gallons in 96 hours. So we want the net rate of flow to be 2/3 gal per hour. 2-x=2/3. x=4/3 choose D.
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A distillate flows into an empty 64-gallon drum at spout A and out of   [#permalink] 09 Oct 2019, 11:46
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