Bunuel wrote:

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. xy/(x+y)

B. (x+y)/(xy)

C. x+y

D. xy

E. x–y

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 jobExample: 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 jobExample: 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 projectSo, 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

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