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# Francis can paint the house by himself in 6 hours, her brother Fred

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Math Expert
Joined: 02 Sep 2009
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Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

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21 Mar 2017, 05:35
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Difficulty:

25% (medium)

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?

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

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Posts: 4132
Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

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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

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Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

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21 Mar 2017, 08:09
If we find the value that all 3 people mentioned do the job "together" in one hour, it actually is equal to the answer of the question;

hence : D
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Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

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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) $$\frac{19}{36}$$
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Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

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