Man-Hours

[Explain this!]

Can the following be sloved by using a man-hours calculation?

10 men can complete a job in 20 hours. 20 men complete the same job in how many hours while working at the same rate?

 

[Steven G]

Can the following be solved by using a man-hours calculation?

Yes. Please share your attempt, if you would like more help.

 

[khansaheb]

Can the following be sloved by using a man-hours calculation?

10 men can complete a job in 20 hours. 20 men complete the same job in how many hours while working at the same rate?

That is about the only way the problem can be solved!

 

[Explain this!]

Yes. Please share your attempt, if you would like more help.

10 men X 20 hours = 200 men-hours. Perhaps divided 10 men X 20 hours = 200 by 20 men X ? hours, and then solve for ?

 

[blamocur]

Perhaps divided 10 men X 20 hours = 200 by 20 men X ? hours, and then solve for ?

Agree.

 

[Explain this!]

Agree.

What would the calculation look like if expressed mathematically?

 

[blamocur]

What would the calculation look like if expressed mathematically?

Not sure what you mean. What are your thoughts ? Also, what is the answer you get?

 

[Explain this!]

Not sure what you mean. What are your thoughts ? Also, what is the answer you get?

If you were giveen a test, and the instructor wants you to show your work (calculation) what would it look like?
I think 10 is the answer.

 

[blamocur]

If you were giveen a test, and the instructor wants you to show your work (calculation) what would it look like?
I think 10 is the answer.

If I were the instructor, your post plus the actual answer would be fine by me. Is your instructor asking for a formula?

 

[Explain this!]

If I were the instructor, your post plus the actual answer would be fine by me. Is your instructor asking for a formula?

No, I am not a student. I was just curious as to how the answer is determined by using the man-hours method.

 

[blamocur]

No, I am not a student. I was just curious as to how the answer is determined by using the man-hours method.

I don't know if there is some standard "man-hours method", and a quick search did not show anything useful.

 

[mmm4444bot]

No, I am not a student. I [am] just curious

Ah, you could have included this at the beginning.

We don't do your homework … Unless you say otherwise, we will treat you like a student working on a school assignment who is stuck at one of the steps.

$\;$

 

[Dr.Peterson]

Can the following be sloved by using a man-hours calculation?

10 men can complete a job in 20 hours. 20 men complete the same job in how many hours while working at the same rate?

10 men X 20 hours = 200 men-hours. Perhaps divided 10 men X 20 hours = 200 by 20 men X ? hours, and then solve for ?

One way to say it neatly, following your thoughts, is this:

The job requires 10 men * 20 hours = 200 man-hours. With 20 men and x hours, the work done will be 20x man-hours. Therefore, we solve 20x = 200 and find that x = 10 hours.​

Is that what you're looking for?

There are other ways, of course. One is to observe that the time is inversely proportional to the number of men, so 10 men/20 men = x hours/20 hours, and x = 20*10/20 = 10 hours.

No, I am not a student. I was just curious as to how the answer is determined by using the man-hours method.

Context is important; it can save a lot of time in discussion.

 

[khansaheb]

......while working at the same rate

rate = constant means man-hours is constant.

Assume that the unknown is

the time to complete the task with 20 men = T (hour) ................... then​

10 (man) * 20 (hours) = 20 (man) * T (hours) → T = 10*20/20 → T = 10 hours

 

[Steven G]

10 men X 20 hours = 200 men-hours. Perhaps divided 10 men X 20 hours = 200 by 20 men X ? hours, and then solve for ?

You double the number of men and therefore you can have the job done in half the time.
For the record you should use people-hours and not men-hours.

 

[Explain this!]

One way to say it neatly, following your thoughts, is this:

The job requires 10 men * 20 hours = 200 man-hours. With 20 men and x hours, the work done will be 20x man-hours. Therefore, we solve 20x = 200 and find that x = 10 hours.​

Is that what you're looking for?

There are other ways, of course. One is to observe that the time is inversely proportional to the number of men, so 10 men/20 men = x hours/20 hours, and x = 20*10/20 = 10 hours.

Context is important; it can save a lot of time in discussion.

Yes, your response is what I am wanting!

 

[Zam]

Can the following be sloved by using a man-hours calculation?

10 men can complete a job in 20 hours. 20 men complete the same job in how many hours while working at the same rate?

If 10 men can complete a job in 20 hours, then they do 1 job in 20 hours.

Now, let's figure out how much of the job one man can do in one hour. One man would take 10 times longer to do 1 job, so:

One man can complete 1 job in 200 hours.
One man can do 1/200 of the job in 1 hour.

If you have 20 men working together, they would complete:

20 men can do 20/200 of the job in 1 hour.
Simplify 20/200 to 1/10.

So, 20 men can complete 1/10 of the job in 1 hour. To complete the whole job (1 job), they'd need:

1 job / (1/10 job per hour) = 10 hours.

Thus, 20 men can complete the job in 10 hours.

 

[Agent Smith]

I don't understand how we can multiply "men" with "hours"?

 

[Agent Smith]

I think this $H_1M_1= H_2M_2$ is correct.

 

[Aion]

I think this $H_1M_1= H_2M_2$ is correct.

When the number of workers increases, the time required to complete the work decreases, assuming they work at the same rate. Specifically, if $T$ is the amount of time and $N$ is the number if workers then $T \propto 1/N$, i.e. they are inversely proportional. If $T_1$ and $T_2$ are the times required when $N_1$ and $N_2$ workers are employed, then $T_1N_1=T_2N_2$. In this case $T_1=20$ hours, $N_1=10$ men, $N_2=20$ men, hence $T_2=10$ hours.