Two turtles, Velma and Justine, were entered into a race.

The equation y = 4x represents Velma's distance in meters, y, after racing for x minutes. The graph below displays Justine's distance and time.

Based on the equation and graph, which two statements below are true?

A. Justine is twice as fast as Velma.
B. Justine is half as fast as Velma.
C. Justine and Velma have the same speed.
D. Justine moves a greater distance than Velma each minute.
E. Justine moves a shorter distance than Velma each minute.

1 answer

To determine which statements are true regarding the speeds of Velma and Justine, we can analyze their rates based on Velma's equation and the graph representing Justine's performance.

  1. Velma's speed: The equation \( y = 4x \) indicates that Velma travels 4 meters for every minute (since for every minute \( x \), the distance \( y \) is increased by 4 meters). Thus, Velma's speed is 4 meters per minute.

  2. Justine's speed: To determine Justine's speed from her graph, we examine her distance at specific times. If the graph shows that Justine's distance is, for example, 6 meters after 1 minute, then her speed would be 6 meters per minute. We would need to evaluate it by looking at her distance over a certain time span.

Now, let's analyze the options based on their speeds:

  • A. Justine is twice as fast as Velma.: If Justine is moving at 8 m/min, then this statement would be true. If she's moving at 6 m/min (or less), it would be false. We need the graph to decide.

  • B. Justine is half as fast as Velma.: This is true if Justine moves at 2 m/min. It requires examination of Justine's speed based on the graph.

  • C. Justine and Velma have the same speed.: This is true if Justine's distance over time equals 4 m/min. We need the graph to decide.

  • D. Justine moves a greater distance than Velma each minute.: This would be true if Justine’s speed exceeds 4 m/min.

  • E. Justine moves a shorter distance than Velma each minute.: This would be true if Justine's speed is less than 4 m/min.

Without the visual representation of Justine's graph, I can't specifically determine her distance or speed values. You would need to identify Justine's speed from the graph to accurately choose which of these statements are true.

In a hypothetical scenario:

  • If Justine is shown to travel 6 meters in 1 minute, then A is true, E is false, and so on.

Please refer to the graph to accurately compare Justine's distance over time to Velma's fixed rate.