Problem Solving

Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)

If Randy can rebuild an automobile engine in a hours. What part of the automobile can he rebuild in 1 hour ? It is 1/a

Similarly, If Alvin can rebuild the same engine in b hours. What part of the automobile can he rebuild in 1 hour ? It is 1/b.

In one hour Randy and Alvin working together can rebuild (1/a + 1/b)th part of an automobile.
Total time taken by Randy and Alvin to rebuild the automobile = 1/(1/a + 1/b) = ab/(a+b) hours

Portion of work Randy completed in ab/(a+b) hours = [ab/(a+b)]*1/a = b/(a+b)
Portion of work Randy will not have to complete = 1 - [b/(a+b)] = a/(a+b)

IMO D

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)

Thanks Anil! That helped.