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The problem provided in the image is in Spanish, and it asks about the speed of a car given a specific function. Here's the problem translated:

**Problem:**  
"The speed \( v(t) \) in km/h at which a car is moving is given by \( R(X) = \frac{3X}{X + 2} \).  
Calculate the time in minutes when the car's speed reaches 6 km/h."

To solve this, follow these steps:

1. **Understand the function:**
   The function given is \( R(X) = \frac{3X}{X + 2} \), which represents the speed \( v(t) \) of the car in km/h as a function of time \( X \).

2. **Set the speed equal to 6 km/h:**
   \[
   \frac{3X}{X + 2} = 6
   \]

3. **Solve for \( X \):**
   Multiply both sides by \( X + 2 \) to eliminate the denominator:
   \[
   3X = 6(X + 2)
   \]

   Expand and rearrange the equation:
   \[
   3X = 6X + 12
   \]
   \[
   3X - 6X = 12
   \]
   \[
   -3X = 12
   \]
   \[
   X = -4
   \]

   However, since \( X \) represents time and time cannot be negative, this result suggests that a mistake may have been made in either the equation setup or in the understanding of the problem. The mistake could stem from incorrectly interpreting or simplifying the equation.

4. **Reevaluate the equation:**
   Let's recheck the equation:
   \[
   \frac{3X}{X + 2} = 6
   \]
   Multiply both sides by \( X + 2 \):
   \[
   3X = 6(X + 2)
   \]
   Distribute on the right-hand side:
   \[
   3X = 6X + 12
   \]
   Subtract \( 6X \) from both sides:
   \[
   -3X = 12
   \]
   Divide by -3:
   \[
   X = -4
   \]

5. **Interpret the result:**
   The calculation suggests \( X = -4 \) but since time cannot be negative, this might indicate that the equation does not reach 6 km/h for any positive time value, or that the model or function provided needs revisiting for physical consistency.

Would you like further clarification or details on any steps? Here are some additional related questions:

1. Could there be a mistake in the interpretation of the speed function \( R(X) \)?
2. How might we redefine the problem to find a positive solution?
3. What physical conditions might lead to a situation where the model suggests a negative time?
4. How does the domain of the function \( R(X) \) impact the solution?
5. What are the limitations of using algebraic models in real-world scenarios?

**Tip:** Always check the domain and range of functions when interpreting real-world problems to ensure physically meaningful results.

¿A qué velocidad v(X) en km/h viaja un automóvil cuando la ecuación R(X) = 3X/(X + 2) y el automóvil tarda 2 minutos en alcanzar una velocidad de 6 km/h?

Learn how to solve the rational speed function R(X) = 3X/(X + 2) to find when a car's speed reaches 6 km/h. This problem covers algebraic concepts involving rational functions and solving for time in real-world scenarios. Suitable for high school students.

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