Three men are working together can finish a house repair job in 10 days. How many days will 5 men working at the same rate finish the same job?

To solve this problem, we can use the concept of man-days, which is the total work done by one person in one day.

Given that three men can finish the job in 10 days, we can calculate the total man-days required to complete the job.

Let's assume that each man can do M man-days of work in one day.

Therefore, three men working together can do 3 x M man-days of work in one day.

Since it takes them 10 days to complete the job, the total work required is 10 x (3 x M) man-days.

Now, let's find the value of M.

We know that the total work required is the same, regardless of the number of men involved. So, if we have 5 men, they should also be able to do 10 x (3 x M) man-days of work in the same amount of time it took the three men.

Therefore, 5 men working at the same rate will finish the job in 10 x (3 x M) / (5 x M) days.

Simplifying the expression, we get 10 x 3 / 5 days, which is equal to 6 days.

Therefore, 5 men working at the same rate will finish the house repair job in 6 days.

To solve this problem, we can use the concept of man-days. A man-day represents the amount of work one person can complete in one day.

Given that three men can finish the house repair job in 10 days, we can calculate the total man-days needed to complete the job. Since there are three men working for 10 days, the total man-days for the job is 3 men x 10 days = 30 man-days.

Now, to find out how many days it would take 5 men to complete the same job, we need to determine the number of days required for 5 men to complete a total of 30 man-days of work.

If the total number of man-days remains constant at 30, and we increase the number of men from 3 to 5, we can set up a proportion to solve for the number of days:

3 men -> 10 days
5 men -> x days

Using the concept of cross-multiplication:

3 men * x days = 5 men * 10 days
3x = 50
x = 50 / 3

Therefore, it would take approximately 16.67 days (rounded to the nearest whole number) for 5 men to complete the same house repair job.

number of "mandays" needed = 3(10) = 30

number of days with 5 men = 30/5 = 6 days