MHB Man-Days and Man-Hours: Understanding Units of Work Measurement

[paulmdrdo1]

If 3 m e n do a job in 12 days and two of the me n are three time s as fast as the third,
how long will it take one of the faster men to do the job ?

this is how I solved it

let x = required time for one of the faster men to do the job alone
3x = time taken by third to finish a job alone.

$\frac{1}{3x}+\frac{1}{3x}+\frac{1}{x}=\frac{1}{12}$

x = 20 days

is this correct?

 

[MarkFL]

No, that's not correct. The way I see it, if would take the slow man $12\cdot7=84$ days to complete the job alone, so one of the faster men would take $$\frac{84}{3}=28$$ days.

You would find this also by using:

$$\frac{1}{3x}+\frac{2}{x}=\frac{1}{12}$$

$$\frac{7}{3x}=\frac{1}{12}$$

$$\frac{3x}{7}=12$$

$$x=28$$

 

[paulmdrdo1]

$12\cdot7=84$ where did you get this?

 

[MarkFL]

The two faster men can do the work of 6 slower men, so having the two faster men and one slow man working is equivalent to 7 slow men working.

 

[paulmdrdo1]

markFL, I saw a solution to this that uses "man-day" which until now I don't have a complete understanding. can you explain about it?

some say that man-day is the work-rate of a single man in one day
some say that it is the amount of work a single person need to complete a job.
some say it is a work-load. which confuses me all the time I encounter these types of problems.

I'm hoping that you could show me the explanation about it. Thanks!

 

[MarkFL]

Simply put, a man-day is the amount of work one man can get done in one day.

You may have heard a more commonly used unit of man-hours. For example, it may be reported to have taken 2,000 man-hours to complete the design of the PCM for the latest hypercar. This may mean 1 man working for 2,000 hours or 2,000 men working for 1 hour, or 4 men working an average of 500 hours each, etc.