Math Problem Statement
Solution
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:
-
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 .
This statement is true.
-
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 = .
- Result: The average speed in the first hour is 40 km/h.
This statement is true.
-
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:
- How do you calculate average speed over multiple intervals with different speeds?
- If the cyclist maintained the same speed for the next 2 hours, how far would they travel?
- What would be the total distance covered if the cyclist maintained 40 km/h for 5 hours?
- How does the slope of the graph relate to the speed at any given time?
- 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!
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Math Problem Analysis
Mathematical Concepts
Graph Interpretation
Speed Calculation
Distance-Time Relationship
Formulas
Speed = Distance / Time
Distance Difference for specific intervals
Theorems
Slope of a Line (indicating speed on distance-time graph)
Suitable Grade Level
Grades 6-9
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