Questions: A construction crew is lengthening a road. The road started with a length of 52 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

A construction crew is lengthening a road. The road started with a length of 52 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
Transcript text: A construction crew is lengthening a road. The road started with a length of 52 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: $\square$ Total length of the road after 38 days: $\square$ miles
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Solution

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Solution Steps

Step 1: Identify the Parameters

The original length of the road is 52 miles, the rate of lengthening is 4 miles per day, and the construction has lasted for 38 days.

Step 2: Write the Equation Relating $L$ to $D$

The equation that relates the total length of the road $L$ after $D$ days of construction to the original length $S$ and the rate of lengthening $R$ is given by: $$L = S + R \cdot D$$

Step 3: Substitute the Given Values into the Equation

Substituting the given values into the equation, we get: $L = 52 + 4 \cdot 38 = 204$ miles.

Final Answer:

The total length of the road after 38 days of construction is 204 miles.

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