Machine A can complete a certain job in x hours. Machine B

Question

Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?

A. (x – y)/(x + y)
B. x/(y–x)
C. (x+y)/xy
D. y/(x-y)
E. y/(x+y)

A) (x – y)/(x + y) 
B) x/(y – x)
C) (x + y)/(xy)
D) y/(x – y) 
E) y/(x + y)

Bunuel · Accepted Answer

Working together A and B complete the job in  \frac{xy}{x+y}  hours (as time is a reciprocal of rate then take the reciprocal of combined rate, which is  \frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy} );

Now, in  \frac{xy}{x+y}  hours A will complete  \frac{1}{x}*\frac{xy}{x+y}=\frac{y}{x+y}  part of the job (rate*time=job) and this will be the part which B will not have to complete.

Answer: E.

sudish · Answer

Since Machine A can complete the job in 'x' hours, the job completed by Machine A in 1 hour will be 1/x

Similarly, since Machine B completes the job in 'y' hours, Machine B will complete 1/y of the job in 1 hour

Hence the job completed in 1 hour when A and B work together at their respective rates is:
1/x + 1/y = (x+y)/xy

Since A completes 1/x of this job, 1/x of the total job is what Machine B will not have to complete because of Machine A's help.

So, the required quantity is (1/x) of (x+y)/xy i.e. (1/x)/(x+y)/xy = xy/x(x+y) = y/(x+y)

Hence, in my opinion, the answer should be option E.

ashimasood · Answer

Not very sure but just thought of the following way:-

A's rate is 1/x
B's rate is 1/y.

when they work together, then work is done in time xy/(x+y).
In this time, work done by b is x/(x+y), by a is y/(x+y) and total work is 1. So the work which b did not do that is the work done by a should be represented as the fraction of total work
a's work/total work =   / 1 = y/(x+y)

Option E

Mindreko · Answer

Plugging in numbers,
Let A rate = 3
B rate = 2
To finish a work of 10,
B would work 5 hours to finish it, but only 4 hours with help of A. So the fraction left is 2/5

Plug in numbers
y/(x+y) = 2/5

Hence E

Hope that helps

Mindreko · Answer

Another approach is algebraic.

Machine A completes a job in x hours so the rate is 1/x
Machine B complets a job in y hours so the rate is 1/y
Collectively 1/x + 1/y = x + y /(xy) for both working together

To get the fraction of what B doesn't have to complete because of A's help is simply to get the fraction of A's workrate when they are both working together

Hence (1/x)/(x+y)/xy = (1/x * xy)/(x+y) = y/(x+y)
Hope that helps again!

sandeeepsharma · Answer

job completed in 1 hour when A and B work together at their respective rates is:
1/x + 1/y = (x+y)/xy

to complete job total time taken = xy/(x+y)

in this time job completed by B= 1/y * xy/(x+y) = x/(x+y)

rest is done by A = 1- X/(x+y)=y/(x+y)

KarishmaB · Answer

Take an example to understand it.
A takes 2 hrs (= x) to complete a work alone and B takes 2 hrs (= y) to complete a work alone. Together, they will complete the work in 1 hr =  
So A does 1/2 of the work in 1 hr (A's rate of work) and B does 1/2 of the work in 1 hr (B's rate of work).

So when they were working together, each needed to work for only 1 hr. 
How much work was done by A in that one hr? 1*(1/2) = (1/2)
So because of A's help, B doesn't need to do half of the work i.e. work done by A.

anjang86 · Answer

My solution might be very simple:

If we pick numbers like x = 3hrs and y = 4hrs then it takes 7hrs to complete two units for both of them. (We can use two units because we are looking for fractional work, not a total quantity #). If it takes 7hrs between the two of them then Ma does 3/7 or the work and Mb does 4/7 of the work. This means that Mb is not doing 3/7 of the work and you can plug in your answer choices to find out which one gives you x=3, y=4 -> 3/7

felixjkz · Answer

This explanation is vague since you picked 1/2. We cannot see how it works because it does not matter what you do with x and y it's around 1/2.
I see that formula is absolutely correct but don't understand why if the value of 1/x is 2/6 and 1/y is 3/6, the portion which y should not do comes out as 3/5 not 2/5.

mbaiseasy · Answer

\frac{1}{x}+\frac{1}{y}=W

Combining their efforts they could finish:  W=\frac{x+y}{xy}

This means it will take them t to complete the job.

\frac{x+y}{xy}(t)=1==>t=\frac{xy}{x+y}

The job done by x will be the job that y doesn't have to worry about.

W=\frac{1}{x}(xy/x+y)==>W=\frac{y}{x+y}

KarishmaB · Answer

The explanation was meant for saswani who had trouble understanding "Then why do we multiply the rate of only A with the total time?"
It doesn't matter what the numbers are - as long as they are easy to work with - you can make out what's going on.

As for your question "why if the value of 1/x is 2/6 and 1/y is 3/6, the portion which y should not do comes out as 3/5 not 2/5."

If x = 3 and y = 2, 
A does 1/3rd work in 1 hr and B does 1/2 work in 1 hr.
When they work together, they complete the work in 1/(1/2 + 1/3) = 6/5 hrs

In 6/5 hrs, A does (1/3)*(6/5) = 2/5 work
and B does (1/2)*(6/5) = 3/5 work

So B does NOT need to do 2/5 of the work. Answer still (E).

KevinBrink · Answer

Can someone please explain the formula xy / x+y to state the work done together. I thought I had a well understanding of this concept, however when I saw this question, I lost it completely. Thanks in advance

Bunuel · Answer

Check here: two-consultants-can-type-up-a-report-126155.html#p1030079 and here: work-word-problems-made-easy-87357.html Hope it helps.

PareshGmat · Answer

.......................... Rate ..................... Time ................. Work Done

Machine A ...............  \frac{1}{x}  ...................... x ........................ 1 (Assumption)

Machine B ................  \frac{1}{y}  ....................... y ....................... 1

Combined rate ............  \frac{1}{x} + \frac{1}{y} = \frac{x+y}{xy}  .............  \frac{xy}{x+y}  ................... 1

Work done due to A's help = Rate of A * Time required for the combined

= \frac{1}{x} * \frac{xy}{x+y} = \frac{y}{x+y}

This will be the benefit for B

Answer = E

Success2015 · Answer

I used the following approach but was not able to proceed, could somebody tell me how/whether we can solve further to get the answer
A = 2 hrs (x), B = 4 hrs(y).
A+B = 4/3 hrs.

If B alone is working, it takes 4 hrs. But both working, B has to work only for 4/3 hours.
So B does not work for 4 hrs - 4/3 hrs = 8/3 hours.

I then thought that B did not have to work for 8/3 hours since A pitched in.
So 8/3 hours multiplied by A's rate (1/2)...gives 4/3..

But none of the options give this value. Any reason this approach does not work?...could somebody pls help.

KarishmaB · Answer

B did not have to work for 8/3 hrs because A pitched in - great. 
So what was the work that B would have done in this 8/3 hrs? Work = Rate*Time = (1/4)*(8/3) = 2/3 (it has to be B's rate)
Option (E) gives you 2/3.
So B did not have to do 2/3rd of the work.

BrentGMATPrepNow · Answer

The earlier posters have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.

If you'd like more information on these approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent

Azim8596 · Answer

ManishaPrepMinds · Answer

I'll solve this using a table with the smart numbers: x= 6 hours for Machine A, y= 4 hours for Machine B, and total work of 12 units.

Information    
     Machine A    
    Machine B    
    Together    
 
    Total work   
   12 units   
   12 units   
   12 units   
 
    Time to complete alone   
   6 hours   
   4 hours   
   ?   
 
    Rate (units/hour)   
   12 ÷ 6 = 2   
   12 ÷ 4 = 3

Time working together

12 ÷ 5 = 2.4 hours   
 
    Work completed by each   
   2 × 2.4 = 4.8 units   
   3 × 2.4 = 7.2 units   
   4.8 + 7.2 = 12 units   
 
    Portion of job completed   
   4.8 ÷ 12 = 2/5   
   7.2 ÷ 12 = 3/5

Therefore, Machine B doesn't have to complete 4.8 units or 2/5 of the job because of Machine A's help   .  
 Substitute x=6, y-=4. This matches our algebraic answer of y/(x+y) = 4/(6+4) = 4/10 = 2/5. 
  Answer E

Machine A can complete a certain job in x hours. Machine B

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Information	Machine A	Machine B	Together
Total work	12 units	12 units	12 units
Time to complete alone	6 hours	4 hours	?
Rate (units/hour)	12 ÷ 6 = 2	12 ÷ 4 = 3
Time working together			12 ÷ 5 = 2.4 hours
Work completed by each	2 × 2.4 = 4.8 units	3 × 2.4 = 7.2 units	4.8 + 7.2 = 12 units
Portion of job completed	4.8 ÷ 12 = 2/5	7.2 ÷ 12 = 3/5

GMAT Problem Solving (PS) Questions

Machine A can complete a certain job in x hours. Machine B

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