Question

A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day.

Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked.
Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 36 days.

Answer 1

L = 4D + 53

After 36 days of work, the road will be 197 miles long.

Explanation:

This question requests that an equation is found to represent the relationship between the length of a road and the days that the workers spend working on the road.

We are given that the road is 53 miles long prior to the work done by the construction crew. This means that this will be added in addition to what we will find.

L represents the length of the road after D days. Since the road is lengthened by 4 miles each day, this could be represented by 4 * D, or simply 4D.

Therefore, the equation we find can be written as L = 4D + 53.

Since we need to find how many miles the road will be after 36 days of work, substitute 36 days as D and solve for L:

L = 4(36) + 53

L = 144 + 53

L = 197

Therefore, the road will be 197 miles long after 36 days of construction.