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

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Math Expert
Joined: 02 Sep 2009
Posts: 46139
Working together, John, David, and Roger require 2 1/4hours to complet [#permalink]

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27 Dec 2015, 10:13
2
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:23) correct 16% (02:21) wrong based on 93 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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Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Re: Working together, John, David, and Roger require 2 1/4hours to complet [#permalink]

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27 Dec 2015, 22:39
1
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

Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 65
Re: Working together, John, David, and Roger require 2 1/4hours to complet [#permalink]

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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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