# Understanding Time and Work

by 22990atinesh
Tags: time, work
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P: 21,313
 Quote by 22990atinesh @Mark44 See your above comment, You also said the same thing. I'm not saying the individual Work rate is total work done/ day or hour. I'm saying Work Rate = Work done by individual / day or an hour.
OK, this is a little closer to being clear. To be more clear, the individual work rate = (work done by the individual)/hour. (Let's get rid of days, and just keep track of time by hours alone. Having days in there as well just confuses the issue.)

What you wrote before, and what I was commenting on, was this:

 Quote by 22990atinesh Rate for 1st set of people ##\frac {M_1D_1H_1}{W_1}##
This is not a rate.
P: 59
 Quote by Mark44 OK, this is a little closer to being clear. To be more clear, the individual work rate = (work done by the individual)/hour. (Let's get rid of days, and just keep track of time by hours alone. Having days in there as well just confuses the issue.) What you wrote before, and what I was commenting on, was this: This is not a rate.
I agree ##\frac {M_1D_1H_1}{W_1}## doesn't represent rate.
P: 59
As far as formula goes I understand that

##\frac {M_1D_1H_1}{W_1}## = ##\frac {M_2D_2H_2}{W_2}## = ##\frac {M_3D_3H_3}{W_3}## = ##k##
is constant. But I do not understand it intuitively. Please explain the intuitive meaning of ##\frac {MDH}{W}## to be constant. Explain it with following example

 A contractor undertook to finish a certain work in 124 days and employed 120 men. After 64 days he found that he had already done ##\frac {2}{3}## rd of the work. How many men can be discharged now so that work may be finished in time ?
Mentor
P: 21,313
 Quote by 22990atinesh As far as formula goes I understand that ##\frac {M_1D_1H_1}{W_1}## = ##\frac {M_2D_2H_2}{W_2}## = ##\frac {M_3D_3H_3}{W_3}## = ##k## is constant. But I do not understand it intuitively.
Which tells me that you don't understand the formula.
Quote by 22990atinesh
Please explain the intuitive meaning of ##\frac {MDH}{W}## to be constant. Explain it with following example

 A contractor undertook to finish a certain work in 124 days and employed 120 men. After 64 days he found that he had already done ##\frac {2}{3}## rd of the work. How many men can be discharged now so that work may be finished in time ?
For the third time, please stop using MDH!!! In problems of this type, the time will normally be given either in days or in hours, but not both.

From the information in the problem here, 120 men have been working 64 days, and have completed 2/3 of the job. The work performed so far represents (120 men) * (64 days) = 120*64 man-days. From this information, how many man-days are required for the entire job?
How many man-days have already been used in the first 64 days?
How much time is left to complete the job?
How many man-days are needed to complete the job?
If you know how many man-days are needed to complete the job, and how many days are left, you should be able to figure out how many men are needed, and therefor, how many can be laid off.

The reason this is so difficult for you, I believe, is that you are trying to pick the "right" formula to use, rather than trying to reason things out. Thinking is always harder than plugging numbers into a formula by rote, which part of the reason that we are 22 posts into this thread.

The only "formula" I'm using here is that "work done" is in units of man-days (in this problem), and is calculated by (work done) = (number of men) * (number of days). If the units of time in the problem had been given in terms of hours, then (work done) would be in units of man-hours. Don't use both hours and days, as in MDH. You'll just confuse yourself.

In an example I gave earlier, "work done" was in units of "square feet that are painted". In this case MDH is meaningless.
P: 59
 Quote by Mark44 Which tells me that you don't understand the formula. For the third time, please stop using MDH!!! In problems of this type, the time will normally be given either in days or in hours, but not both. From the information in the problem here, 120 men have been working 64 days, and have completed 2/3 of the job. The work performed so far represents (120 men) * (64 days) = 120*64 man-days. From this information, how many man-days are required for the entire job? How many man-days have already been used in the first 64 days? How much time is left to complete the job? How many man-days are needed to complete the job? If you know how many man-days are needed to complete the job, and how many days are left, you should be able to figure out how many men are needed, and therefor, how many can be laid off. The reason this is so difficult for you, I believe, is that you are trying to pick the "right" formula to use, rather than trying to reason things out. Thinking is always harder than plugging numbers into a formula by rote, which part of the reason that we are 22 posts into this thread. The only "formula" I'm using here is that "work done" is in units of man-days (in this problem), and is calculated by (work done) = (number of men) * (number of days). If the units of time in the problem had been given in terms of hours, then (work done) would be in units of man-hours. Don't use both hours and days, as in MDH. You'll just confuse yourself. In an example I gave earlier, "work done" was in units of "square feet that are painted". In this case MDH is meaningless.
Thanx Mark44, I think I get it. You are trying to say that total Man hour/unit work is constant i.e. MH/W=k. for example we have given that 2 Men working 3 hours/day works for 4 days to complete a work (unit of work). Calculate how many days required by 1 man working 2 hours/day to complete the 1/2 of that work.

Sol: As we know Man hour/unit work is constant. Hence ## \frac{M_1H_1}{W_1} = \frac {M_2H_2}{W_2}##
Now we can easily plug data in LHS of the above equation. But for RHS as we know, we have to calculate days required by 1 man working 2 hours/day to complete the 1/2 of that work. so we have to double the total Man hour in RHS i.e.

## \frac{2*(4*3)}{1} = \frac{2*(1*(X*2))}{1}##

## \frac{2*(4*3)}{1} = \frac{1*(X*2)}{1/2}##

##X=6##

Correct If I did something wrong.

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