To determine the unit rate of the faster horse, let's analyze both horses' speeds.

Given Information

1. Horse A: The equation $y = 580x$ describes the distance $y$ in meters that Horse A can cover in $x$ minutes. The unit rate (speed) of Horse A is the coefficient of $x$, which is 580 meters per minute.

2. Horse B: The graph shows the distance covered by Horse B over time. We need to find the slope of the line in the graph to determine Horse B's speed, as the slope represents distance per unit time (meters per minute).

Analyzing Horse B's Graph

The graph has points we can use to find the slope:

• At $x = 1$ minute, $y = 600$ meters.
• At $x = 3$ minutes, $y = 1800$ meters.

Using these two points, we can calculate the slope $m$ (rate of Horse B): $m = \frac{\Delta y}{\Delta x} = \frac{1800 - 600}{3 - 1} = \frac{1200}{2} = 600 \text{ meters per minute}$

Conclusion

• Horse A's speed: 580 meters per minute.
• Horse B's speed: 600 meters per minute.

Since 600 meters per minute is greater than 580 meters per minute, Horse B is the faster horse.

Answer

The unit rate of the faster horse (Horse B) is 600 meters per minute.

Would you like further details or have any questions?

Additional Questions

1. What would the distance be for each horse after 10 minutes?
2. How would you calculate the time taken for Horse A to cover a distance of 3000 meters?
3. If Horse B maintained its speed for 20 minutes, how far would it travel?
4. What does the slope represent in a distance-time graph?
5. How could we determine which horse is faster just by looking at their slopes on a graph?

Tip

Remember, the slope in a distance-time graph directly shows the speed, making it easy to compare rates by looking at the steepness of each line.