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Francis can paint the house by herself in 6 hours, her brother Fred ca

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Bunuel
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Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   17 Mar 2017, 03:11
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Francis can paint the house by herself 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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D
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appu2693
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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   17 Mar 2017, 07:05
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Bunuel wrote:
Francis can paint the house by herself 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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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   17 Mar 2017, 07:06
appu2693 wrote:
Bunuel wrote:
Francis can paint the house by herself 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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Option D - 19/36

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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   17 Mar 2017, 08:15
Francis can paint the house in 6 hours.
So in 1 hour she can paint \(\frac{1}{6}\) of the house

Fred can paint the house in 4 hours.
So in 1 hour he can paint \(\frac{1}{4}\) of the house

Frank can paint the house in 9 hours.
So in 1 hour he can paint \(\frac{1}{9}\) of the house

If they all work together then in 1 hour the fraction of the house they can paint = \(\frac{1}{6}+\frac{1}{4}+\frac{1}{9}\)=\(\frac{6+9+4}{36}\)=\(\frac{19}{36}\)

Answer D
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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   20 Mar 2017, 07:23
Fraction of the house painted in one hour= 1/6+1/4+1/9
=19/36

Correct answer is D
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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   20 Mar 2017, 07:30
Bunuel wrote:
Francis can paint the house by herself 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 unit

Francis's efficiency is 6 units/hr
Fred's efficiency is 9 units/hr
Frank's efficiency is 4 units/hr

Combined efficient is 19 units/hr

So, in 1 hour the 19/36 units of the house will be painted, answer must be (D)
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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   21 Mar 2017, 04:09
Bunuel wrote:
Francis can paint the house by herself 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


Rate of Francis, Fred and Frank = 1/6, 1/4 and 1/9 respectively
Combined rate = 1/6 + 1/4 + 1/9 = 19/36

work completed in 1 hr = 19/36 * 1 = 19/36
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Re: Francis can paint the house by herself in 6 hours, her brother Fred ca [#permalink] New post   25 Apr 2022, 05:10
Hello from the GMAT Club BumpBot!

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