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# QOTD # 13 Three pumps, P, R, and T, working simultaneously a

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QOTD # 13 Three pumps, P, R, and T, working simultaneously a [#permalink]  10 Sep 2016, 01:43
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Question Stats:

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Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours. Pumps P and R, working simultaneously at their respective constant rates, can fill the tank in 7 hours. How many hours will it take pump T, working alone at its constant rate, to fill the tank?

A) 1.7
B) 10.0
C) 15.0
D) 17.5
E) 30.0

Practice Questions

Question: 13
Page: 199
[Reveal] Spoiler: OA

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Re: QOTD # 13 Three pumps, P, R, and T, working simultaneously a [#permalink]  10 Sep 2016, 01:46
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Explanation

Working simultaneously pumps P and R fill $$\frac{1}{7}$$ of the tank in 1 hour. Working simultaneously, the three pumps fill $$\frac{1}{5}$$ of the tank in 1 hour. Therefore, working alone, pump T fills $$\frac{1}{5} - \frac{1}{7}$$ or $$\frac{2}{35}$$ of the tank in 1 hour. Thus, working alone, pump T takes $$\frac{35}{2}$$ hours, or 17.5 hours, to fill the tank.

The correct answer is Choice D.
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Re: QOTD # 13 Three pumps, P, R, and T, working simultaneously a [#permalink]  11 Sep 2016, 14:01
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Carcass wrote:
Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours. Pumps P and R, working simultaneously at their respective constant rates, can fill the tank in 7 hours. How many hours will it take pump T, working alone at its constant rate, to fill the tank?

A) 1.7
B) 10.0
C) 15.0
D) 17.5
E) 30.0

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let’s use these rules to solve the question. . . .

Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours
So, by Rule #1, pumps P, R and T working together can complete 1/5 of the job in ONE HOUR

Pumps P and R, working simultaneously at their respective constant rates, can fill the tank in 7 hours
So, by Rule #1, pumps P, and R working together can complete 1/7 of the job in ONE HOUR

So, pump T's contribution in ONE HOUR = 1/5 - 1/7
= 7/35 - 5/35
= 2/35

So, in ONE HOUR, pump T can complete 2/35 of the job
By Rule #2, then, it will take pump T 35/2 hours to complete the ENTIRE JOB

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Re: QOTD # 13 Three pumps, P, R, and T, working simultaneously a [#permalink]  24 Nov 2018, 01:04
Pumb P and R working together and complete in 7 Hours
PR / P+R = 7 --- Step 1
All 3 pumps together complete in 5 Hours
1/P+ 1/R + 1/T = 1/5 --- Step 2
(R+P)/(PR) + 1/T = 1/5
So (R+P)/(PR) = 1/7 --- From Step 1
1/7 + 1/T = 1/5 -- Substitue in Step 3
1/T = 1/5 - 1/7
1/T = 2/35
T = 35/2 = 17.5 -- ANSWER
Re: QOTD # 13 Three pumps, P, R, and T, working simultaneously a   [#permalink] 24 Nov 2018, 01:04
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