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

Question

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

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

CounterSniper · Accepted Answer

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

Skywalker18 · Answer

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

EMPOWERgmatRichC · Answer

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

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

ksrutisagar · Answer

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

BrentGMATPrepNow · Answer

One approach is to assign a "nice" value to the entire job.
So let's use a number that works well with the two given values of 9 hours and 6 hours. 
Let's say the job consists of making  54  widgets.

Working alone, R can complete a certain kind of job in 9 hours.  
In other words, R can make  54  widgets in 9 hours.
This means R's RATE = 6 widgets per hour

R and S, working together at their respective rates, can complete one of these jobs in 6 hours  
In other words, R and S can make  54  widgets in 6 hours.
This means their COMBINED rate = 9 widgets per hour

9 - 6 = 3
So, S's RATE =   3   widgets per hour

In how many hours can S, working alone, complete one of these jobs?  
Another words, how much time will it take S to make  54  widgets?

Time = output/rate 
So, time =  54 /  3   = 18 hours

Answer: A

Cheers,
Brent

d999 · Answer

1/6- 1/9 = 1/18 ( rate)
Reciprocal is 18 ( hours)

alexandy43 · Answer

The answer is A - 18, but how we come to this?

1/9 + 1/6 = 18

But how did we get 18 here?

gurmukh · Answer

It is 
1/6-1/9 = 1/18

So S efficiency is 1/18 therefore will complete the job in 18 hrs

Posted from my mobile device

alexandy43 · Answer

yeah, i got that it is 1/18

But 1/6 - 1/9 = 1/-3 ? no? 
Where the number 18 appeared?

gurmukh · Answer

No it is not, that how you don't subtract it.
Take the lCM of denominator that is 18 then it goes in 6 three times and in 9 two times so 3-2 =1
Therefore subtracting value is 1/18

alexandy43 · Answer

Where the number 18 appeared?

No it is not, that how you don't subtract it.
Take the lCM of denominator that is 18 then it goes in 6 three times and in 9 two times so 3-2 =1
Therefore subtracting value is 1/18

ah i see

thank you man!!!

ScottTargetTestPrep · Answer

We can create the equation:

1/S + 1/9 = 1/6

Multiplying by 18S, we have:

18 + 2S = 3S

18 = S

Answer: A

Snehaaaaa · Answer

Working alone R can complete the job in 1/9 hours
Working together R and S can complete the job in 6 hours i.e.
1/R + 1/S =1/6
Substituting 1/R
therefore, 1/9+1/S=1/6
or,1/S=1/6-1/9
1/S=1/18
Correct answer is A

Amritaachopra17 · Answer

While I got the question right, is it just me or the language is warped? What does it mean by completing one of these jobs? especially when we are assuming both parties (R and R+S) are doing the same job.

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

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

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