If it takes Jacob \(x\) hours to complete a project and it takes Mike \(y\) hours to complete the same project, how many

VJesus12 wrote: ↑

Mon Nov 09, 2020 8:27 am

If it takes Jacob \(x\) hours to complete a project and it takes Mike \(y\) hours to complete the same project, how many hours will it take them to complete the project if they are working together?

A. \(\dfrac{xy}{x+y}\)

B. \(\dfrac{x+y}{xy}\)

C. \(x+y\)

D. \(xy\)

E. \(x-y\)

Answer: A

Source: Veritas Prep

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let’s use these rules to solve the question. . . .

It takes Jacob x hours to complete a project and it takes Mike y hours to complete the same project
So, applying Rule #1....
Jacob completes 1/x of the job in ONE HOUR
Mike completes 1/y of the job in ONE HOUR
So, in ONE HOUR, the two workers complete 1/x + 1/y of the job

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

In other words, in ONE HOUR, the two workers complete (x + y)/xy of the job
Applying Rule #2, the total time to COMPLETE the job = xy/(x + y)

Answer: A

Cheers,
Brent