# Math Help - 42 men can do a work in 15 days, how many men for 21 days?

1. ## 42 men can do a work in 15 days, how many men for 21 days?

Q25: If 42 men can do a work in 15 days, how many men are required to
complete it in 21 days?
A. 24
B. 36
C. 30
D. None of these
how?

I would try to solve $\displaystyle \frac{42}{15} = \frac{x}{21}$

3. Originally Posted by pickslides

I would try to solve $\displaystyle \frac{42}{15} = \frac{x}{21}$
Then $x = 58.8$?

I'm not very good at this either.
But in my analysis, in 1 day, $\frac{1}{15}$ of the job is done by 42 men. This means that 1 man does $\frac{1}{630}$ of the job in one day.

In 21 days, a man does $\frac{21}{630}$ of the job. From here, it should be easy to know how many men are needed to get the job done in 21 days.

So I don't think (a) is the correct answer here.

4. Well it really depends on if there is any scaling involved in this problem. For example the more workers you have, the less number of days a job should take relatively.

This could be determined if an additional ratio/information was given.

But as this was posted in the pre-uni/pre-algebra thread I thought some simple ratios will do the job. My pick is option D.

Q25: If 42 men can do a work in 15 days, how many men are required to
complete it in 21 days?
A. 24
B. 36
C. 30
D. None of these
how??????????????????????????
1. If 42 men need 15 days then 42 * 15 men will finish the work in 1 day.

2. If you distribute the work of this one day on 21 days you need:

$\dfrac{42 \cdot 15}{21} = 30$

Q25: If 42 men can do a work in 15 days, how many men are required to
complete it in 21 days?
A. 24
B. 36
C. 30
D. None of these
how?
You will need 5 times as many men to get the job done in a fifth of the time.
Hence 210 men get the job done in 3 days.
One seventh of the men will take 7 times as long.
30 men are needed to take 21 days.

Q25: If 42 men can do a work in 15 days,
how many men are required to do it in 21 days?

. . (A) 24 . . (B) 36 . . (C) 30 . . (D) None of these

In 15 days, 42 men can do the job.

In one day, 42 men can do $\frac{1}{15}$ of the job.

In one day, one man can do $(\frac{1}{42})(\frac{1}{15}) = \frac{1}{630}$ of the job.

In 21 days, 1 man can do $(21)(\frac{1}{630}) = \frac{1}{30}$ of the job.

Therefore, it takes 30 men to do the job in 21 days.

8. Yet another way of thinking about it: 21 days is $\frac{21}{16}= \frac{7}{5}$ of the 15 days required by 42 men. Since more men would take less time and vice-versa, this is an "inverse" proportion- invert the fraction. 21 days will require $\frac{5}{7}(42)= 5(6)= 30$ men.

(Pickslides was treating it as a direct proportion.)

9. Here's another "sideways glance" on this.

Suppose there was only 1 guy.
We'd need 42 of him to get the job done in 15 days.
So, in 15 days he'd have had to do 42 times as much work as he ordinarily can do.
Therefore, he needs 42 days to do what 42 guys do in 1 day.
So he needs 42(15) days to do what 42 guys do in 15 days.
That's 630 days.

In 21 days, he'd need to do the work of 30 guys each day.

Or, it takes 42(15)=630 man-days to complete the work.

In 21 days, 30 men are required.