# T&W q5

#### Saumyojit

##### Senior Member
24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, what is the number of men required to finish the same work in 6 days?

1 men is working for 1920 hr to complete work.
(80 hrs) 10 days = 1 work

24 men in 8 hrs= 1/80 work

1 man in 1 day (8hr) = 1/1920 work

1 man in 1 day(1hr)= 1/(1920* 8)

1 man in 1 day(10hr )= 1/1536 of work

(x* 1/1536) * 60= 1
x= 1536/60= 25

Where am I wrong?

#### Jomo

##### Elite Member
What is the difficulty here.

The job takes 1920 hours to complete.

You want to complete it in 6 days---192hrs/6days = 32hr/day.
That is, the total numbers of hours worked in each day must be 32 hours.
You want each worker to work 10 hours per day.

Can you finish from here?

#### Jomo

##### Elite Member
24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, what is the number of men required to finish the same work in 6 days?

1 men is working for 1920 hr to complete work.
(80 hrs) 10 days = 1 work

24 men in 8 hrs= 1/80 work

1 man in 1 day (8hr) = 1/1920 work

1 man in 1 day(1hr)= 1/(1920* 8)

1 man in 1 day(10hr )= 1/1536 of work

(x* 1/1536) * 60= 1
x= 1536/60= 25

Where am I wrong?
1 men is working for 1920 hr to complete work.
(80 hrs) 10 days = 1 work

I will replace 1920 hours with 1 work
So 80 hrs*10days =1920hrs.
Dividing by 80 hrs I get 10days = 24. 10 days equal 24 what?????
This means that (80 hrs) 10 days = 1 work can't be correct

24 men in 8 hrs= 1/80 work NO! 24 men in 8hr will do 1/10 of the job.

1 man in 1 day(1hr)= 1/(1920* 8) Write what you mean! 1 man in 1 hr = 1/(1920*8)

#### Saumyojit

##### Senior Member
@pka @Jomo @Dr.Peterson

1 man is individually giving 8 hrs per day and total 80 hrs per one man out of 24 in finishing the work so 24 men are all contributing 1920 hrs
Now for x men to finish a work in 60 hrs it means each one out of those x will be spending 60 hrs in that work. SO (x*60 hrs) will give me man hours for 2nd case
but how will i know that x* 60 hrs = ?

#### Dr.Peterson

##### Elite Member
24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, what is the number of men required to finish the same work in 6 days?
The work requires 24 men * 8 hours/day * 10 days = 1920 man-hours.

x men working for 10 hours a day for 6 days put in x * 10 hours/day * 6 days = 60x man-hours.

To finish the work, we need 60x = 1920, so x = 1920/60 = 32 men.

What part of this don't you understand?

#### Jomo

##### Elite Member
what does 80 hour * 10 day imply?
You tell us! You were the one who wrote it in you post

(80 hrs) 10 days = 1 work

Now I realize that you meant 80hrs = 10 days = 1 work.
Please write what you mean unless some simple people like me will easily get confused.

#### Saumyojit

##### Senior Member
60x = 1920
x* 60 hrs = 1920 hr
how will i know that 1920 hrs is the man hours for those x men who are working 10 hrs per day for 6 days total
as 1920 hrs are the MAN hours for 24 men working 8hrs per day.

Is man hour always same for any given diff cases ? Why then

#### Jomo

##### Elite Member
If 10 people work 4 hours per day for 5 days to do a job, then the job requires 10people*4hrs/day*5day= 200 people-hours
This means it will take i person 200 hours to do the job

If 7 people work 6 hours per day for 11 days to do a job, then the job requires 7 people*6hrs/day*11day= 462 people-hours.
This means that it will take 1 person 464 hours to do the job.

So no, man-hrs are not always the same.

#### Saumyojit

##### Senior Member
x* 60 hrs = 1920 hr
that is what i am telling , if man-hrs are not always the same then how do i know before knowing x that
x* 60 hrs = 1920 hr

#### Jomo

##### Elite Member
24 men working 8 hours a day can finish a work in 10 days----24men*8hrs/day*10days =1920 man-hrs. This means that it will take 1 man 1920 hours to do the job and it also means that the job requires 1920 man-hours.

Working at the rate of 10 hours a day, what is the number of men required to finish the same work in 6 days. Let x be the number of men needed.
Then x men*10hrs/day*6days = 60x man-hours.

What you are missing is that the job, regardless of how many men are working, regardless of how many hours these men work per day and regardless of how many days the men work for, will require 1920 man-hours to complete.

therefore 60x man-hours = 1920 man-hours or 60x=1920 or x=32

To be even clearer, if you add up the total number of hours all the men worked for, regardless of how many men were working, it will be 1920 hours.
For some days there may be 3 men working for 4 hours and another day 11 men working for 6 hours and 3 other men working for 3 hours,..... When the job is completed there would have been 1920 hours that it took the men to complete this job.

#### Saumyojit

##### Senior Member
it also means that the job requires 1920 man-hours.
ok .

If 10 people work 4 hours per day for 5 days to do a job, then the job requires 10people*4hrs/day*5day= 200 people-hours
This means it will take i person 200 hours to do the job

If 7 people work 6 hours per day for 11 days to do a job, then the job requires 7 people*6hrs/day*11day= 462 people-hours.
This means that it will take 1 person 464 hours to do the job.
Here you say man hrs are not always same .

Are they doing same job or different jobs then?

#### Saumyojit

##### Senior Member
ok .

Here you say man hrs are not always same .

Are they doing same job or different jobs then?
@Jomo

#### Dr.Peterson

##### Elite Member
ok .

Here you say man hrs are not always same .

Are they doing same job or different jobs then?
I think he was referring to the fact that different jobs require different amounts of work. That's not really relevant to solving this problem, which assumes that this job will always require 1920 man-hours (or person-hours, if the problem hadn't specified men).

Of course, that is really an assumption. In real life, people may work with different efficiencies at different times of day, or for longer hours, or when working in different groups (e.g. helping one another or fighting one another), so that man-hours are just an approximation. The problem is idealized, like all word problems! (I'm reminded of a famous book I read long ago.)

#### Saumyojit

##### Senior Member
I think he was referring to the fact that different jobs require different amounts of work. That's not really relevant to solving this problem, which assumes that this job will always require 1920 man-hours (or person-hours, if the problem hadn't specified men).

Of course, that is really an assumption. In real life, people may work with different efficiencies at different times of day, or for longer hours, or when working in different groups (e.g. helping one another or fighting one another), so that man-hours are just an approximation. The problem is idealized, like all word problems! (I'm reminded of a famous book I read long ago.)
ok in one job man hours are always same