Question
The distance traveled by the blue car is represented by
y
=
79
x
y=79x .
The distance traveled by the red car was monitored by a table. Click Here for Help Video.
Number of Hours
Miles Traveled
6
6
444
444
7
7
518
518
8
8
592
592
The speed of the blue car is
miles per hour.
The speed of the red car is
miles per hour.
The
car is faster.
Answers
GPT-4o mini
To find the speed of each car, we need to analyze the information given for both the blue and red cars.
1. **Speed of the blue car:**
The equation for the distance traveled by the blue car is given by \( y = 79x \), where \( y \) is the distance in miles and \( x \) is the time in hours. The coefficient 79 represents the speed of the blue car. Thus, the speed of the blue car is:
\[
\text{Speed of the blue car} = 79 \text{ miles per hour}
\]
2. **Speed of the red car:**
The distances traveled by the red car at different hours are:
- At 6 hours: 444 miles
- At 7 hours: 518 miles
- At 8 hours: 592 miles
Now, we can calculate the speed of the red car:
- From 6 to 7 hours:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{518 - 444}{7 - 6} = \frac{74}{1} = 74 \text{ miles per hour}
\]
- From 7 to 8 hours:
\[
\text{Speed} = \frac{592 - 518}{8 - 7} = \frac{74}{1} = 74 \text{ miles per hour}
\]
So the speed of the red car is:
\[
\text{Speed of the red car} = 74 \text{ miles per hour}
\]
3. **Comparing speeds:**
- Speed of the blue car = 79 miles per hour
- Speed of the red car = 74 miles per hour
Since \( 79 > 74 \), we can conclude:
\[
\text{The blue car is faster.}
\]
### Summary:
- The speed of the blue car is **79 miles per hour**.
- The speed of the red car is **74 miles per hour**.
- The **blue car is faster**.
1. **Speed of the blue car:**
The equation for the distance traveled by the blue car is given by \( y = 79x \), where \( y \) is the distance in miles and \( x \) is the time in hours. The coefficient 79 represents the speed of the blue car. Thus, the speed of the blue car is:
\[
\text{Speed of the blue car} = 79 \text{ miles per hour}
\]
2. **Speed of the red car:**
The distances traveled by the red car at different hours are:
- At 6 hours: 444 miles
- At 7 hours: 518 miles
- At 8 hours: 592 miles
Now, we can calculate the speed of the red car:
- From 6 to 7 hours:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{518 - 444}{7 - 6} = \frac{74}{1} = 74 \text{ miles per hour}
\]
- From 7 to 8 hours:
\[
\text{Speed} = \frac{592 - 518}{8 - 7} = \frac{74}{1} = 74 \text{ miles per hour}
\]
So the speed of the red car is:
\[
\text{Speed of the red car} = 74 \text{ miles per hour}
\]
3. **Comparing speeds:**
- Speed of the blue car = 79 miles per hour
- Speed of the red car = 74 miles per hour
Since \( 79 > 74 \), we can conclude:
\[
\text{The blue car is faster.}
\]
### Summary:
- The speed of the blue car is **79 miles per hour**.
- The speed of the red car is **74 miles per hour**.
- The **blue car is faster**.