Problem Solving

Q. 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)

I don't know the answer to this question, experts out there please advise.

Speed Machine A 1/x, Speed Machine B 1/y; If A and B work together at their cumulative rate is (x+y)/xy. The following represents the fraction of the job that B will not have to complete because of A's help -> B will not have to complete the A's contribution or 1/x; 1/x :(divided by) (x+y)/xy= 1/x * xy/(x+y)= y/(x+y)

IOM e

MI3 wrote:Q. 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)

I don't know the answer to this question, experts out there please advise.

Since it's possible that x>y or that y>x, any answer choice that includes y-x (which is negative if x>y) or x-y (which is negative if y>x) can be eliminated.
Eliminate A, B and D.

Let x=2 hours and y=2 hours.
Since A and B take the same amount of time to complete the job alone, each works at the same rate.
Thus, when A and B work together, each will complete 1/2 the job.
Thus, the fraction of the work not completed by B = 1/2. This is our target.

Now we plug x=2 and y=2 into C and E to see which yields our target of 1/2.

Only answer choice E works:
y/(x+y) = 2/(2+2) = 2/4 = 1/2.

The correct answer is E.