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To create the graphs for both fish, we’ll consider their movements based on their unique abilities and the provided time intervals. Let's break down each scenario and plot points to represent their distances over time.

### Part (a) Teleporting Fish:
- **From 0 to 20 seconds**: The Teleporting Fish stays at the start line, so its distance from the start, \( d(t) \), remains at 0 meters.
- **At 20 seconds**: The Teleporting Fish warps instantly to the midpoint of the track, which is 50 meters.
- **From 20 to 40 seconds**: It stays at the midpoint, so \( d(t) \) remains at 50 meters.
- **At 40 seconds**: The Teleporting Fish warps instantly to the finish line, which is 100 meters.
- **From 40 to 60 seconds**: It stays at the finish line, so \( d(t) \) remains at 100 meters.

### Part (b) Instant-Speed Fish:
- **From 0 to 20 seconds**: The Instant-Speed Fish moves at a constant speed of 2.5 m/s. Over 20 seconds, she covers:
  \[
  d = 2.5 \, \text{m/s} \times 20 \, \text{s} = 50 \, \text{meters}
  \]
  So, at 20 seconds, she reaches the midpoint (50 meters).
- **From 20 to 40 seconds**: She rests at the midpoint, so \( d(t) \) remains at 50 meters.
- **From 40 to 60 seconds**: She resumes her speed of 2.5 m/s for another 20 seconds, covering another 50 meters and reaching the finish line at 100 meters.

### Graphing the Motion
The graphs for each fish’s distance \( d(t) \) over time \( t \) should have steps that reflect their pauses and instantaneous jumps in distance.

Would you like me to illustrate the graphs, or do you have further questions about each step? 

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1. What would the graph look like if the teleporting fish had more frequent warps?
2. How would the graph change if the instant-speed fish had acceleration instead?
3. What if the race were 200 meters long with the same rules?
4. How would a delay in starting time affect each fish's graph?
5. Could the instant-speed fish beat the teleporting fish with different speeds?

**Tip:** In distance-time graphs, horizontal lines indicate periods of rest, while vertical jumps indicate instantaneous changes in position.

In a 100 m fish race, there are two competitors: Teleporting Fish and Instant-Speed Fish. Graph the motion of each fish based on the described behaviors.

Learn how to graph the distance-time motion of two unique competitors in a 100-meter fish race. This example demonstrates concepts like instantaneous position changes, constant speed, and interpreting distance-time graphs, suitable for students in Grades 6-8.

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