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 38 days. equation: total length of the road after 38 days: miles

Explanation:

Step1: Form the equation

The initial length is 53 miles, and each day 4 miles are added. So the total length \( L \) is the initial length plus 4 times the number of days \( D \). So the equation is \( L = 53 + 4D \).

Step2: Substitute \( D = 38 \)

Substitute \( D = 38 \) into the equation \( L = 53 + 4D \). First calculate \( 4\times38 = 152 \), then add 53: \( L = 53 + 152 = 205 \).

Answer:

Equation: \( L = 53 + 4D \)
Total length of the road after 38 days: 205 miles