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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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Question Stats:
74% (01:12) correct 26% (01:22) wrong based on 167 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
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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
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02 Oct 2018, 06:27