Math Problem Statement
Solution
To identify the mistakes Albert made on the distance-time graph based on his cycling journey, let’s break it down:
Albert’s Journey:
- Cycled 3 km in 8 minutes.
- Stopped at a friend's house for 10 minutes.
- Cycled the remaining 2 km to school in 12 minutes.
Analyzing the Graph:
From this description and the list of possible mistakes, here is how to check the graph:
-
Missing units from the time axis:
The graph needs time labels with proper units (e.g., minutes or hours). If they are missing, this is a mistake. -
Missing units from the distance axis:
Similarly, the distance axis should clearly state units (e.g., km). -
The horizontal section should be shorter:
- Albert stopped for 10 minutes, so the graph’s horizontal line (indicating no movement) should span exactly 10 minutes.
- If it is longer than 10 minutes, this is incorrect.
-
The horizontal section should be longer:
- If the horizontal line is too short (less than 10 minutes), this would also be an error.
-
The line should not start at 11:00:
- Albert left home at 11:00. If the graph starts before this time, it is a mistake.
Next Steps:
Look closely at the graph and check:
- Are the units on both axes present?
- Does the horizontal section correctly represent 10 minutes?
- Does the graph start at 11:00?
Would you like me to analyze this further step-by-step with explanations?
Related Questions:
- How do you draw an accurate distance-time graph for this journey?
- How do you calculate speed from a distance-time graph?
- What does a horizontal line mean on a distance-time graph?
- How can we correct Albert’s mistakes in this graph?
- Why is it important to include units on graph axes?
Tip: A slope on a distance-time graph represents the speed—steeper slopes indicate faster movement.
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Math Problem Analysis
Mathematical Concepts
Distance-Time Graphs
Graph Interpretation
Units on Axes
Formulas
Speed = Distance / Time
Slope = Rise / Run
Theorems
The slope of a distance-time graph represents speed
Horizontal sections indicate no movement
Suitable Grade Level
Grades 6-8