The time it takes to lay a sidewalk of a certain type varies directly as the length and inversely as the number of men working. If eight men take two days to lay 100 feet, how long will three men take to lay 150 feet?

To solve this problem, we can use the concept of direct and inverse variation.

Let's denote the time it takes to lay the sidewalk as T, the length of the sidewalk as L, and the number of men working as M.

According to the problem, the time T varies directly with the length L and inversely with the number of men M. This can be expressed as:

T ∝ L/M

We are given that when 8 men work, it takes 2 days to lay 100 feet of sidewalk. We can use this information to form a proportion:

(8/3) = (2/T) = (100/150)

Simplifying this proportion, we find:

8T = 6 T = 6/8 T = 3/4

Therefore, it will take three men (M = 3) to lay 150 feet (L = 150) in 3/4 of a day (T = 3/4).

As this question has both direct and inverse variation in it, let's do one part at a time:

Inverse variation means as one quantity increases the other decreases. If the number of men increases, the time taken to lay the sidewalk will decrease.

Find the constant: When 8 men lay 100 feet in 2 days:

We see that it will take more days, as we expected.

Now for the direct variation. As one quantity increases, the other also increases. It will take longer for the three men to lay 150 feet than 100 feet. The number of men stays the same.

For 3 men laying 150 feet, the time will be