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)

Answer 1

E) y / ( x + y )

Explanation:

Machine A need x hours to do the job

Then in one our machine A do 1/x of the job

Machine B need y hours to do the job

Then in one hour machine B do 1/y of the job

Then the two machines working together in one our time will make:

1/x + 1/ y = ( y + x ) xy

And the fraction of the job B does not need to do, since it was done by machine A is

( 1/x ) / (y + x ) / xy = y / ( x + y )