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

Expert's post

00:00

Question Stats:

77% (01:28) correct
22% (02:20) wrong based on 18 sessions

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?

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

Expert's post

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.

Re: QOTD # 13 Three pumps, P, R, and T, working simultaneously a [#permalink]
11 Sep 2016, 14:01

Expert's post

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

Answer: D

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