X men can do a piece of work in 21 days working 8 hours each day. The number of days taken by x men is 70% of the number of days taken by (x-1)men, working 6 hours a day. Find the value of x.

Answer 1

First find the expression for the total amount of man-hours it takes to complete the project. We are given that it takes 21 days for some number, X, of men to complete at 8 hours per day.

So every day there are 8*X hours worked. In 21 days, 8X*21 hours are worked.

This gives us a total amount of 168X man-hours worked, because 8*21=168, and we still don't know how many men that is.

21 is 70% of the days it takes the different group to finish. As an equation this is shown as 21=(0.7)*D

D is the new amount of days. Solve for D we get D=21/(0.7) = 30.

It takes 30 days for the other group to finish the work.

The project takes the same amount of man-hours to finish.

With the new information we have 30 days, X-1 men, and 6 hours worked per day.

we do the same thing as before, 30*6*(X-1). This gives us 180(X-1) man-hours.

Since the man-hours stays the same, we can say that 168X = 180(X-1)

Now we solve for X. First expand the right side of the equation to get:

168X = 180X - 180

Next add 180 to both sides to get:

168X+180 = 180X

Next subtract 168X from both sides to get:

180 = 12X

Finally divide both sides by 12 to isolate X:

15 = X

So now we know X is 15 men.