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# The Best Performer

## Question

Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.

So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive. Edited by ShadowAngel7
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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.

So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive.

essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with

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Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.

So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive.

essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with

Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.

It is straightforward to construct a linear equation

Bx = y

where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively.

[1,] 0.02614608

[2,] 0.03372183

[3,] 0.04013209

[4,] 0.01705517

Units are project/day. From here, it is simple to compute how much each individual contributes to a project.

##### Share on other sites

• 0

Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

In each scenario, 1 worker is excluded and everyone else contributes.

Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task.

How many days does each person contribute to the total project days?

Individuals don't contribute to the project's time.

A can do a project, alone, in a days, but a does not increase the time of a project.

Rather, 1/a contributes to the reciprocal of the project's time.

1/a +1/b+1/c = 1/10, etc.

Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.

So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive.

essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with

Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.

It is straightforward to construct a linear equation

Bx = y

where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively.

[1,] 0.02614608

[2,] 0.03372183

[3,] 0.04013209

[4,] 0.01705517

Units are project/day. From here, it is simple to compute how much each individual contributes to a project.

I like your answer. It is interesting how in America this problem is solved differently from my home country.

##### Share on other sites

• 0

Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.

It is straightforward to construct a linear equation

Bx = y

where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively.

[1,] 0.02614608

[2,] 0.03372183

[3,] 0.04013209

[4,] 0.01705517

Units are project/day. From here, it is simple to compute how much each individual contributes to a project.

I like your answer. It is interesting how in America this problem is solved differently from my home country.

I'm intrigued. How do people from your country solve this problem?

##### Share on other sites

• 0

Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.

It is straightforward to construct a linear equation

Bx = y

where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively.

[1,] 0.02614608

[2,] 0.03372183

[3,] 0.04013209

[4,] 0.01705517

Units are project/day. From here, it is simple to compute how much each individual contributes to a project.

I like your answer. It is interesting how in America this problem is solved differently from my home country.

I'm intrigued. How do people from your country solve this problem?

• 1
• 1

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