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The problem provided describes a construction scenario where workers are extending a road that initially measures 51 kilometers. They add 1 kilometer to the road each day, and the goal is to create an equation relating the length \( L \) of the road in kilometers to the number of days \( D \) of construction.

### Step 1: Writing the Equation
The initial length of the road is 51 kilometers, and the road grows by 1 kilometer each day. Therefore, after \( D \) days of construction, the length \( L \) of the road can be expressed as:

\[
L = 51 + D
\]

### Step 2: Calculating the Length After 35 Days
To find the length of the road after 35 days, we substitute \( D = 35 \) into the equation:

\[
L = 51 + 35 = 86 \text{ kilometers}
\]

Thus, after 35 days, the length of the road will be **86 kilometers**.

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Would you like more details or have any questions about this solution?

Here are 5 related questions to explore further:
1. How would the equation change if the workers added 2 kilometers each day?
2. How long will the road be after 50 days of construction?
3. If the road needs to be 100 kilometers long, how many days will the workers need to work?
4. What happens if the workers stop extending the road after 20 days—what would be the final length?
5. How can this problem be modeled graphically to represent the relationship between \( D \) and \( L \)?

**Tip:** For linear growth problems like this, the rate of change (in this case, 1 kilometer per day) is a key component of the equation.

Un grupo de obreros está alargando una carretera que inicialmente medía 51 kilómetros. Añaden un kilómetro a la carretera cada día. Dejen que L represente la longitud (en kilómetros) después de D días de construcción. Escribir una ecuación que relacione L con D. Luego utilizar esta ecuación para hallar la longitud de la carretera después de 35 días.

This problem explores a linear growth scenario where workers extend a road by adding 1 kilometer each day. Starting with an initial length of 51 kilometers, students will learn how to model this situation algebraically and calculate the total length after a given number of days, like 35 days.

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