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Working alone, R can complete a certain kind of job in 9 hours. R and

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Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 18 Nov 2015, 00:18
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Question Stats:

83% (01:04) correct 17% (01:28) wrong based on 195 sessions

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Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?

(A) 18
(B) 12
(C) 9
(D) 6
(E) 3

Project PS Butler : Question #103


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Re: Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 18 Nov 2015, 00:29
working together R and S can complete the job in 6 hours
which means
1/R + 1/S =1/6
R can complete the job in 9 hours
therefore, 1/9+1/S=1/6
or,1/S=1/6-1/9
1/S=1/18
Thus S working alone can complete the job in 18 hours
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Re: Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 18 Nov 2015, 00:32
Let total time taken by S to complete the job = S
total time taken by R to complete the job = 9
Work done by R in an hour
1/R = 1/9

Working together R and S can complete the job in 6 hours
1/R + 1/S = 1/6
=>1/S = 1/6 - 1/R
= 1/6 - 1/9
= 1/18
=> S = 18 hours

Answer A
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Re: Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 29 Nov 2015, 13:08
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Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

Here, we're told that R can complete a job in 9 hours and that R and S (when working together) can complete a job in 6 hours. We're asked how long it takes S to complete the job alone.

The 'twist' here is that we have to 'work back' to find the value of S...

(9)(S)/(9 + S) = 6

9S = 54 + 6S
3S = 54
S = 18 hours

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Re: Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 27 Dec 2018, 11:34
Bunuel wrote:
Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?

(A) 18
(B) 12
(C) 9
(D) 6
(E) 3

Project PS Butler : Question #103


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if r and s be the amount of work done by R and S in 1 hour respectively.

then r=1/9 & r+s = 1/6 so s= 1/6-1/9 = 1/18

hence ans A
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Re: Working alone, R can complete a certain kind of job in 9 hours. R and  [#permalink]

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New post 27 Dec 2018, 23:24
R alone : 9 hours

R and S together : 6 hours

S alone = ?

It can easily be seen that if S = 9, R and S = 4.5

Since R and S = 6, S is more than 9 i.e 12 or 18 from the answer choices

We know that time taken by R and S = \(\frac{(RS)}{(R+S)}\),

If we substitute R = 9, and S = 12 in the above formula, We get \(\frac{(9*12)}{(9+12)}\)

By inspection this is not an integer

So, We are left with S= 18

Choice A
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Re: Working alone, R can complete a certain kind of job in 9 hours. R and   [#permalink] 27 Dec 2018, 23:24
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