a construction crew is lengthening a road. the road started with a length of 52 miles, and the crew is adding 2 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 39 days.

equation:
total length of the road after 39 days: miles

Question

a construction crew is lengthening a road. the road started with a length of 52 miles, and the crew is adding 2 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 39 days.

equation:
total length of the road after 39 days:   miles

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Algebraic Expressions" ], "new_concepts": [ "Linear Equations" ], "current_concepts": [ "Algebraic Translation", "Algebraic Expressions", "Linear Equations" ] } ## Identify the initial value and rate of change $$ \begin{aligned} &\text{Initial length} = 52\ &\text{Rate of change} = 2\text{ miles per day} \end{aligned} $$ ## Formulate the linear equation $$ L = 52 + 2D $$ ## Calculate the total length after 39 days $$ \begin{aligned} D &= 39\ L &= 52 + 2(39)\ L &= 52 + 78\ L &= 130 \end{aligned} $$ A construction crew is lengthening a road. The road started with a length of 52 miles, and the crew is adding 2 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 39 days. Equation: $L = 52 + 2D$ Total length of the road after 39 days: 130 miles { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the initial value and rate of change

Formulate the linear equation

Calculate the total length after 39 days

Answer: