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
If it takes Jacob \(x\) hours to complete a project and it takes Mike \(y\) hours to complete the same project, how many
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
For work questions, there are two useful rules:VJesus12 wrote: ↑Mon Nov 09, 2020 8:27 amIf 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
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