https://file.aiquickdraw.com/mathbot/file/1726340572699e6gg05on.jpg

To analyze this problem, let's break it down based on the graph and the provided statements:

### Graph Information:
- **X-axis**: Duration of the journey in hours.
- **Y-axis**: Distance traveled in kilometers.

### Analyzing Each Statement:

1. **La distance parcourue lors de la dernière demi-heure de course est 20 km.**
   - We can check this by observing the last half-hour on the graph, i.e., between 4 and 4.5 hours.
   - The distance at 4 hours is approximately 180 km, and at 4.5 hours, it is 200 km.
   - **Result**: The distance traveled in the last half-hour is \(200 - 180 = 20 \, \text{km}\).  
   **This statement is true**.

2. **La vitesse moyenne lors de la première heure est de 40 km/h.**
   - We can check this by looking at the distance after the first hour.
   - At 1 hour, the distance covered is approximately 40 km.
   - Speed = Distance/Time = \( \frac{40 \, \text{km}}{1 \, \text{h}} = 40 \, \text{km/h} \).
   - **Result**: The average speed in the first hour is 40 km/h.  
   **This statement is true**.

3. **Le cycliste a parcouru les cent premiers kilomètres en 3h.**
   - We check when the cyclist reaches 100 km on the graph.
   - At 3 hours, the cyclist has traveled approximately 100 km.
   - **Result**: The cyclist covered the first 100 km in 3 hours.  
   **This statement is true**.

### Conclusion:
All three statements are **true** based on the graph.

Would you like more detailed calculations or explanations? Here are five related questions to expand your understanding:

1. How do you calculate average speed over multiple intervals with different speeds?
2. If the cyclist maintained the same speed for the next 2 hours, how far would they travel?
3. What would be the total distance covered if the cyclist maintained 40 km/h for 5 hours?
4. How does the slope of the graph relate to the speed at any given time?
5. How can you use graphs like these to predict future motion?

**Tip**: When interpreting graphs, the slope of the line gives you the rate of change—in this case, the speed of the cyclist!

The cyclist's distance traveled graph and analysis of statements regarding the journey.

Learn how to interpret a distance-time graph and determine the accuracy of statements regarding the cyclist's journey. Analyze speed, distance, and time relationships to check the validity of statements about the last half-hour, first hour, and total distance traveled.

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