A construction crew is lengthening a road. The road started with a length of 57 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 31 days.

Accepted Solution

The equation you can use to relate L to D uses the information in the first part of the problem. First, if we just add 4 miles every day (ignoring the other piece), the length of the road would be 4 times the number of days, or L = 4D. But since we started with 57 miles built, we have to add that in order to get the total length, so the equation would be:

L = 4D + 57

You can use this question to find any value of L or D if you know one of them. According to the questoin, we know the crew worked 34 days (or D). So if you plug in 34 for D you'll get:

L = 4(34) + 57 ->
L = 136 + 57 ->
L = 193