On a bicycle, Courtney rides for 5 hours and is 42 miles from her house. After riding for 9 hours, she is 74 miles away.

What is Courtney's rate?

To find Courtney's rate of travel, we can use the formula for rate:

\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}}
\]

We are given two data points for her travel:

1. After 5 hours, she is 42 miles away.
2. After 9 hours, she is 74 miles away.

### Step 1: Calculate the distance traveled between these two points
From the dataTo find Courtney's rate of travel, we can use the formula for rate:

\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}}
\]

We are given two data points for her travel:

1. After 5 hours, she is 42 miles away.
2. After 9 hours, she is 74 miles away.

### Step 1: Calculate the distance traveled between these two points
From the 
- At 9 hours, Courtney is 74 miles away.
- At 5 hours, she is 42 miles away.

So, the distance traveled between these two times is:
\[
\text{Distance traveled} = 74 \, \text{miles} - 42 \, \text{miles} = 32 \, \text{miles}
\]

### Step 2: Calculate the time taken to travel that distance
The time difference between 9 hours and 5 hours is:
\[
\text{Time difference} = 9 \, \text{hours} - 5 \, \text{hours} = 4 \, \text{hours}
\]

### Step 3: Calculate her rate
Now, use the formula for rate:
\[
\text{Rate} = \frac{32 \, \text{miles}}{4 \, \text{hours}} = 8 \, \text{miles per hour}
\]

So, Courtney's rate is **8 miles per hour**.

Would you like further details or clarifications?

### Related Questions:
1. What if Courtney continued riding for 12 hours? How far would she be?
2. If she rides at the same rate, how long will it take to reach 100 miles?
3. What is the total distance she would cover after 7 hours?
4. How would her rate change if she had traveled 50 miles in 6 hours?
5. Can you represent Courtney's movement as a linear function?

**Tip:** Always pay attention to units of time and distance when calculating rates!

On a bicycle, Courtney rides for 5 hours and is 42 miles from her house. After riding for 9 hours, she is 74 miles away. What is Courtney's rate?

Find out how to calculate Courtney's bicycle riding rate using basic algebra. She rides 42 miles in 5 hours and 74 miles in 9 hours. Learn step-by-step how to use the distance and time formula to find her speed, ideal for students in Grades 6-8.

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