If it takes Jacob x hours to complete a project and it

Hi All,

We're told that it takes Jacob X hours to complete a project and it takes Mike Y hours to complete the same project. We're asked for the number of hours it would take them to complete the project if they worked together. This is a great 'concept' question; if you recognize the concepts involved, you can actually answer it without doing any calculations.

When 2 entities (people, machines, etc.) work on a task together for the same amount of time, you can the Work Formula to determine how long it takes them to complete the task:

Work = (A)(B)/(A+B) where A and B are the two individual times it takes to complete the job

Here, we have two people working for the same amount of time, so we know that the Work Formula will apply. This gives us (X)(Y)/(X+Y).

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: Veritas Prep

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

A. xy/(x+y)
B. (x+y)/xy
C. x+y
D. xy
E. x-y

The OA is A

Jacob’s rate is 1/x, and Mike’s rate is 1/y. We can create the following combined rate expression:

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

Since time is the inverse of rate, it will take them xy/(x+y) hours to complete the project.

Answer: A