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

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If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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17 Apr 2018, 05:14
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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

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Re: If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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17 Apr 2018, 06:02
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

$$\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$$

$$z = \frac{xy}{(x+y)}$$

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If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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18 Apr 2018, 17:45
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

Jacob's 1 hour's work = 1/x
Mike's 1 hour's work=1/y

Jacob and Mike's 1 hour's work=1/x + 1/y
= (x+y)/xy

Now (x+y)/xy is done in 1 hour
So, the entire work will be done by = xy/(x+y), which is option A.
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Re: If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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19 Apr 2018, 16:50
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

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

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Re: If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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25 Aug 2018, 07:02
Top Contributor
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 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)

Cheers,
Brent
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Re: If it takes Jacob x hours to complete a project and it takes Mike y  [#permalink]

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29 Dec 2018, 12:44
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).

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Re: If it takes Jacob x hours to complete a project and it takes Mike y   [#permalink] 29 Dec 2018, 12:44
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