Math Problem Statement

Use the graph to determine which runner had the greater speed.

Solution

The graph shows the motion of two runners, labeled as Runner #1 and Runner #2, plotting their distance (in meters) over time (in seconds). To determine which runner has the greater speed, we need to compare their slopes.

  • Speed is the slope of the distance-time graph (speed = distance/time).
  • The steeper the slope, the greater the speed.

Analysis:

  • Runner #1 has a steeper line than Runner #2, meaning Runner #1 covers more distance in the same amount of time.
  • Therefore, Runner #1 has the greater speed.

The correct answer is Runner #1.

Would you like a detailed explanation of how speed relates to the slope in more depth?

Here are 5 related questions to consider:

  1. How can you calculate speed from a distance-time graph?
  2. What does a flat line in a distance-time graph represent?
  3. How would the graph look if one of the runners were to slow down over time?
  4. How can you calculate the speed difference between the two runners?
  5. What would the graph look like if both runners had the same speed?

Tip: When comparing speeds on a graph, the steeper the slope, the faster the object is moving!

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Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Speed Calculation
Linear Relationships

Formulas

Speed = Distance / Time

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8