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Working together, John, David, and Roger require 2 1/4hours to complet

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Working together, John, David, and Roger require 2 1/4hours to complet  [#permalink]

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New post 27 Dec 2015, 10:13
2
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A
B
C
D
E

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  5% (low)

Question Stats:

89% (01:44) correct 11% (02:48) wrong based on 104 sessions

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Working together, John, David, and Roger require \(2 \frac{1}{4}\) hours to complete a certain task, if each of them works at his respective constant rate. If John alone can complete the task in \(4 \frac{1}{2}\) hours and David alone can complete the task in 9 hours, how many hours would it take Roger to complete the task, working alone?

A. 2 1/3
B. 4 1/2
C. 6 3/4
D. 9
E. 12

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Re: Working together, John, David, and Roger require 2 1/4hours to complet  [#permalink]

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New post 27 Dec 2015, 22:39
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Bunuel wrote:
Working together, John, David, and Roger require \(2 \frac{1}{4}\) hours to complete a certain task, if each of them works at his respective constant rate. If John alone can complete the task in \(4 \frac{1}{2}\) hours and David alone can complete the task in 9 hours, how many hours would it take Roger to complete the task, working alone?

A. 2 1/3
B. 4 1/2
C. 6 3/4
D. 9
E. 12


(J+D+R)(9/4)=1
J+D+R= 4/9

(2/9 + 1/9 + R) = 4/9
R=1/9

9 hours

Answer: D
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Re: Working together, John, David, and Roger require 2 1/4hours to complet  [#permalink]

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New post 07 Aug 2017, 23:17
\(R_J\)+\(R_R\)+\(R_R\)=\(\frac{Job}{Time}\) = \(\frac{1}{2.25}\)

\(R_J\)=\(\frac{Job}{Time}\) =\(\frac{1}{4.5}\)

\(R_D\)=\(\frac{Job}{Time}\) =\(\frac{1}{9}\)

Combining the last 3 equations we can compute the rate of Roger :

\(R_R\)=\(\frac{1}{9}\)=\(\frac{Job}{Time}\) =\(\frac{1}{T}\)

so T = 9

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Re: Working together, John, David, and Roger require 2 1/4hours to complet   [#permalink] 07 Aug 2017, 23:17
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