Question

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)

Answer 1

D
`(a)/((a+b))`

Explanation:

In here, it does not matter which time, "a" or "b", is bigger than the other. It only matters to know which portion of “a” will be reduce by adding Alvin's effort. So the previous already let us know that formula is “a” between something else, it means, a fraction from “a”, that for this case is given by the sum of the score of both rates, “a” and “b”, since the denominator of this fraction must include the elements involved.

In summary, the portion of job that Randy won’t have to do is given by,
`(a)/((a+b))`

In case We wanted to know the opposite, the portion of work Alvin won’t have to do, We would´ve used
`(b)/((a+b))`.

Regards!