SOLUTION: A certain job can be done by 72 men in 100 days. There were 80 men at the start of the project but after 40 days, 30 of them had to be transferred to another project. How long wil

Question 1208470: A certain job can be done by 72 men in 100 days. There were 80 men at the start of the project but after 40 days, 30 of them had to be transferred to another project. How long will it take the remaining workforce to complete the job?
Found 5 solutions by ikleyn, greenestamps, josgarithmetic, math_tutor2020, Edwin McCravy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A certain job can be done by 72 men in 100 days. There were 80 men at the start of the project
but after 40 days, 30 of them had to be transferred to another project.
How long will it take the remaining workforce to complete the job?
~~~~~~~~~~~~~~~~~~~~~~

Since the job can be done by 72 men in 100 days, it means that the entire job is 72*100 = 7200 man-days. 80 men in 40 days completed 3200 man-days of the job; the remaining job is 7200-3200 = 4000 man-days. The remaining workforce is 80-30 = 50 men. They will complete the remaining part of the gob in 4000/50 = 80 days. ANSWER

Solved.

========================

If you read my solution and the solution by @greenestamps attentively, then with no doubts
you will see that they are very similar. We use similar words and similar construction of
the solution.

It is because problems of this kind are very old: they trace their lineage back to the times
of Ancient Egypt.

During many years and many centuries, people rolled their solutions in the same way
as the surf rolls stones, making them ideally smooth.

This form of solutions, which @greenestamps and me used in our posts, were formed verbally
in the last 300 years.

So, when @greenestamps and me re-tell this classic solution, we use the same words, the same form
and the same ideas as in ancient times or in the last 300 years.

This is a tribute to the tradition of retelling old solutions for old problems in an old wrapper - as a standard classic mantra.

It is good if you retell it to your teacher in the same words - the teacher will see that you
not only know the solution, but know and follow traditions, too.

May be, in 20 years later you will re-tell it to your children and in 50 years later will re-tell to your
grandchildren. In this sense, it is good to know the tradition and to pass it to the next generations.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The job requires 72 men working 100 days; the number of man-days required for the job is 72*100 = 7200.

80 men working for the first 40 days perform 80*40 = 3200 man-days of labor. The number of man-days remaining to complete the job is 7200-3200=4000.

The remaining 4000 man-days of labor, performed by 80-30=50 men, requires an additional 4000/50 = 80 days.

ANSWER: 80 days

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

N, how many workers
R, work rate for any one worker
T, time
J, how many jobs

------------------------

First sentence

Second sentence
x for the unknown number of days
80 men for 40 days and then 50 men for x days
The work to be done is 1 job.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 80 days

Explanation

Consider a warehouse with 72000 boxes.
There are 72 men who can move these boxes in 100 days.
Assume that none of the workers hinder one another.
Each man would move 72000/72 = 1000 boxes.
Each man has a unit rate of 1000/100 = 10 boxes per day.

1 man can move 10 boxes per day.
80 men can move 80*10 = 800 boxes per day.
Over the course of 40 days, that would be 800*40 = 32000 boxes.
There are 72000-32000 = 40000 boxes remaining.

The 80-man crew drops to 50 since 30 people transfer.
x = number of days to move 40,000 boxes
1 man can move 10 boxes per day
50 men can move 50*10 = 500 boxes per day
500x = number of boxes to move
500x = 40000
x = 40000/500
x = 80

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

I think this type problem should be considered as a problem in VARIATION. Common sense tells us that: Time (t) increases as the amount of job-doing (j) increases. Time (t) decreases as the number of workers (w) increases. Therefore, time (t) varies directly as the amount of job-doing (j) and inversely as the number of workers (w). That is: -----------------------------------------
A certain job [THAT'S 1 JOB] can be done by 72 men in 100 days.
Solve for k So
There were 80 men at the start of the project
but after 40 days,....
So for those first 40 days, So the amount of job-doing during those first 40 days was 4/9ths of a job. So that means there is still 5/9 of a job left to be done.
.....30 of them had to be transferred to another project.
So the amount of job-doing left for the remaining 50 men to do was 5/9 of a job. Answer: 80 days. Edwin

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