https://file.aiquickdraw.com/mathbot/file/1730203017042vbtv5v37.jpg

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.

The distance y in meters that can be covered by Horse A in x minutes can be represented by the equation y = 580x. The distance that can be covered by Horse B is shown on the graph. Determine the unit rate of the faster horse.

Find out how to determine the unit rate of the faster horse using distance-time data. This problem involves calculating the speed of two horses, Horse A with a known equation y = 580x, and Horse B whose data is plotted on a graph. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation