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Francis can paint the house by himself in 6 hours, her brother Fred
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21 Mar 2017, 05:35

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Difficulty:

15% (low)

Question Stats:

74% (00:50) correct 26% (00:54) wrong based on 130 sessions

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Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

Re: Francis can paint the house by himself in 6 hours, her brother Fred
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21 Mar 2017, 08:02

Top Contributor

Bunuel wrote:

Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36 B. 1/19 C. 1/2 D. 19/36 E. 36/19

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. . . .

Francis can paint the house by himself in 6 hours From Rule #1, we know that, in ONE HOUR, Francis can paint 1/6 of the house

Fred can paint the house in 4 hours From Rule #1, we know that, in ONE HOUR, Fred can paint 1/4 of the house

Frank can paint the house in 9 hours From Rule #1, we know that, in ONE HOUR, Frank can paint 1/9 of the house

If they all worked together, what fraction of the house would be painted after ONE HOUR? Add each person's contribution for ONE HOUR: 1/6 + 1/4 + 1/9 = 6/36 + 9/36 + 4/36 = 19/36

Re: Francis can paint the house by himself in 6 hours, her brother Fred
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21 Mar 2017, 08:37

Bunuel wrote:

Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36 B. 1/19 C. 1/2 D. 19/36 E. 36/19

Let the total work be 36 units...

Efficiency of Francis is 6 units/hour Efficiency of Fred is 9 units/hour Efficiency of Frank is 4 units/hour

Combined efficiency of Francis , Fred and Frank is 19 units

So, part of house that would be painted after one hour is \(\frac{19}{36}\)

Thus, answer must be (D) \(\frac{19}{36}\) _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

Francis can paint the house by himself in 6 hours, her brother Fred
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02 Oct 2018, 06:27

House painted by Francis in an hour=1/6 House painted by Fred in an hour=1/4 House painted by Frank in an hour=1/9 House painted by Francis, Fred and Frank in an hour=1/6+1/4+1/9= 19/36 (work/hour)

(D)

gmatclubot

Francis can paint the house by himself in 6 hours, her brother Fred &nbs
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02 Oct 2018, 06:27