1. **State the problem:** We have three runners each running at a constant speed. We want to determine which runner runs the fastest based on their distance-time data. 2. **Recall the formula for speed:** Speed is the rate of change of distance with respect to time, given by $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ Since each runner runs at a constant speed, their speed is the slope of the distance vs. time graph or the constant ratio from the table or equation. 3. **Analyze Runner #1:** The graph shows a straight line passing through points like (10,50), (20,100), (30,150), (40,200), (50,250), (60,300). Calculate speed using any point, for example (10,50): $$\text{speed}_1 = \frac{50}{10} = 5 \text{ meters/second}$$ 4. **Analyze Runner #3:** From the table, pick any point, for example (9,45): $$\text{speed}_3 = \frac{45}{9} = 5 \text{ meters/second}$$ Check another point to confirm constant speed, e.g., (60,300): $$\frac{300}{60} = 5 \text{ meters/second}$$ So Runner #3 also runs at 5 meters/second. 5. **Analyze Runner #2:** The equation is given as $$d = 6.5t$$ This means Runner #2's speed is the coefficient of $t$: $$\text{speed}_2 = 6.5 \text{ meters/second}$$ 6. **Compare speeds:** - Runner #1 speed = 5 m/s - Runner #3 speed = 5 m/s - Runner #2 speed = 6.5 m/s 7. **Conclusion:** Runner #2 runs the fastest because 6.5 m/s is greater than 5 m/s. Therefore, **Runner #2 is the fastest runner.**