Answer:
With 21 men working, it will take 20 days to finish the same job .
Step-by-step explanation:
This problem is an example of work and rate word problems.
To solve this problem by getting first the amount of work that one person does in one day.
We can do this by simply multiplying the number of men needed to do the job in a given time period.
After getting the amount of work that one person does in one day, we can set up an equation with a variable and let that variable be the value we are looking for.
Solution:
amount of work that one person does in one day = 15 men * 28 days
amount of work that one person does in one day = 420 man-days
Let x be the number of days needed to finish the same job using 21 men
- 21 * x = 420 man-days
- 21x = 420 man-days
- x = 420 man-days / 21 men
- x = 20 days
Note that we equate 420 man-days to the new condition because it is said in the problem that the job to be done is still the same. Notice also that the unit man is cancelled and we are left with the unit of time (days).
Therefore, it will take 20 days to finish the job if it is to be done by 21 men.
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