MHB Work Word problem - linear equation

[paulmdrdo1]

Forty men were engaged to finish a work in 90 days.
Afer 60 days, some men stopped working.
The remaining men finished the job at a same rate in 40 more days.
How many men stopped?

this is how far I can get to

let x = number of men remained
40-x = number of men stopped

Please help. thanks!

 

[I like Serena]

Forty men were engaged to finish a work in 90 days.
Afer 60 days, some men stopped working.
The remaining men finished the job at a same rate in 40 more days.
How many men stopped?

this is how far I can get to

let x = number of men remained
40-x = number of men stopped

Please help. thanks!

Hi paulmdrdo!

How many man-days in total does it take to finish the work?
How are the man-days actually spent? That should sum up to the total.

 

[paulmdrdo1]

working together they are required to do the job in 90 days.

so their rate of work is 1/90 per day. but I don't know how to get their individual rate.
and also what do you mean by "man-day" ? is it a day an individual working alone?
please help.

 

[I like Serena]

working together they are required to do the job in 90 days.

so their rate of work is 1/90 per day. but I don't know how to get their individual rate.
and also what do you mean by "man-day" ? is it a day an individual working alone?
please help.

Yes, a man-day is the work an individual does when working alone.
Since the job takes 90 days with 40 men together, the total number of man-days is $40 \cdot 90 = 3600$.
That means that their individual rate is 1/3600 per day instead of 1/90.

So 40 men working for 60 days complete $40\cdot 60$ man-days.
Summed with the men, that remain working, times 40 days must come out as the total number of man-days.

 

[paulmdrdo1]

$40(90)=40(60)+40(40-x)$

x=10 men stopped working.

"man-day" is confusing me. is it a day a single person required to get the job done or is it the work done in a day by a single person? which is which? can you explain more.

sorry bear with me. English is not my mother language. thanks!

 

[soroban]

Hello, paulmdrdo!

Forty men were engaged to finish a work in 90 days.
Afer 60 days, some men stopped working.
The remaining men finished the job at a same rate in 40 more days.
How many men stopped?

Let x = number of men who stopped.

Forty men were expected to do the job in 90 days.
But they worked only 60 days.
So they did only \tfrac{60}{90} \,=\,\tfrac{2}{3} of the job.

In one day, the 40 men could do \tfrac{1}{90} of the job.
In one day, one man could do \tfrac{1}{3600} of the job.
In 40 days, one man could do \tfrac{40}{3600} \,=\,\tfrac{1}{90} of the job.

In 40 days, the remaining 40-x men can do \tfrac{40-x}{90} of the job.
But this task was the other \tfrac{1}{3} of the job.

Hence: .\frac{40-x}{90} \:=\:\frac{1}{3}

Got it?

 

[I like Serena]

$40(90)=40(60)+40(40-x)$

x=10 men stopped working.

Good!

"man-day" is confusing me. is it a day a single person required to get the job done or is it the work done in a day by a single person? which is which? can you explain more.

sorry bear with me. English is not my mother language. thanks!

A man-day is the work done in a day by a single person.

 

[paulmdrdo1]

how is "man-day" different from "work-rate"?

 

[I like Serena]

how is "man-day" different from "work-rate"?

A man-day is the work-rate of one man per day.

Work-rate is a more general term, which does not have to be for one man nor for one day.