Question

25
The distance traveled by the blue car is represented by
𝑦
=
54
𝑥
y=54x .



The distance traveled by the red car was monitored by a table. Click Here for Help Video.



Number of Hours
Miles Traveled
5
5
245
245
6
6
294
294
7
7
343
343


The speed of the blue car is
miles per hour.



The speed of the red car is
miles per hour.



The
car is faster.

Answer 1

To determine the speeds of the blue car and the red car, we can analyze the given equations and data.

1. **Blue Car:**
The distance traveled by the blue car is given by the equation:
\[
y = 54x
\]
Here, \( y \) represents the distance traveled in miles and \( x \) represents the time in hours. The speed of the blue car can be directly inferred from this equation:
\[
\text{Speed of the blue car} = 54 \text{ miles per hour}
\]

2. **Red Car:**
To find the speed of the red car, we'll analyze the table provided:

| Number of Hours (x) | Miles Traveled (y) |
|---------------------|---------------------|
| 5 | 245 |
| 6 | 294 |
| 7 | 343 |

To calculate the speed, we can take the total miles traveled divided by the number of hours for the data points given. We can calculate the average speed based on the total miles and total time for any complete data points. Let's use the last point for simplicity where \( x = 7 \) hours and \( y = 343 \) miles.

\[
\text{Speed of the red car} = \frac{\text{Miles Traveled}}{\text{Number of Hours}} = \frac{343}{7} = 49 \text{ miles per hour}
\]

3. **Comparison:**
Now we've calculated both speeds:
- Speed of the blue car: 54 miles per hour
- Speed of the red car: 49 miles per hour

Therefore, we can conclude:
- The speed of the blue car is **54 miles per hour**.
- The speed of the red car is **49 miles per hour**.
- The **blue car** is faster.