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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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New post 17 Apr 2018, 04:14
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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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New post 17 Apr 2018, 05:02
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


\(\frac{1}{x} + \frac{1}{y} = \frac{1}{z}\)

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

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

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New post 18 Apr 2018, 16:45
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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New post 19 Apr 2018, 15:50
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.

Answer: 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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New post 25 Aug 2018, 06:02
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)

Answer: A

Cheers,
Brent
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Re: If it takes Jacob x hours to complete a project and it takes Mike y &nbs [#permalink] 25 Aug 2018, 06:02
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