Math Problem Statement

Albert left home at 11:00 and cycled 3 km at a constant speed in 8 minutes, then stopped at a friend's house for 10 minutes, before cycling the remaining 2 km to school in 12 minutes. Identify all the mistakes in Albert's distance-time graph.

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:

  1. Cycled 3 km in 8 minutes.
  2. Stopped at a friend's house for 10 minutes.
  3. 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:

  1. 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.

  2. Missing units from the distance axis:
    Similarly, the distance axis should clearly state units (e.g., km).

  3. 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.
  4. The horizontal section should be longer:

    • If the horizontal line is too short (less than 10 minutes), this would also be an error.
  5. 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:

  1. How do you draw an accurate distance-time graph for this journey?
  2. How do you calculate speed from a distance-time graph?
  3. What does a horizontal line mean on a distance-time graph?
  4. How can we correct Albert’s mistakes in this graph?
  5. 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