https://file.aiquickdraw.com/mathbot/file/1729237066600vmmvpoz2.jpg

To solve the problem, we need to calculate Amy's average speed based on the distance Jessica ran and the time Amy took to cover that distance. Here's the step-by-step breakdown:

### Step 1: Calculate the distance Jessica ran.
Jessica runs in two parts:
- For 15 minutes at 6 miles per hour
- For 40 minutes at 9 miles per hour

We need to convert the times to hours since speed is in miles per hour (mph):
- 15 minutes = \( \frac{15}{60} = 0.25 \) hours
- 40 minutes = \( \frac{40}{60} = 0.67 \) hours

#### Distance for each part:
1. **First part**: Distance = Speed × Time
   \[
   \text{Distance}_1 = 6 \, \text{mph} \times 0.25 \, \text{hours} = 1.5 \, \text{miles}
   \]

2. **Second part**: 
   \[
   \text{Distance}_2 = 9 \, \text{mph} \times 0.67 \, \text{hours} = 6.03 \, \text{miles}
   \]

#### Total distance Jessica runs:
\[
\text{Total distance} = 1.5 + 6.03 = 7.53 \, \text{miles}
\]

### Step 2: Calculate Amy's average speed.
Amy takes 45 minutes to run the same distance. First, convert 45 minutes to hours:
\[
\text{Time for Amy} = \frac{45}{60} = 0.75 \, \text{hours}
\]

Now, use the formula for average speed:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Time}}
\]
\[
\text{Average speed for Amy} = \frac{7.53 \, \text{miles}}{0.75 \, \text{hours}} = 10.04 \, \text{mph}
\]

### Final Answer:
Amy's average speed is approximately **10.04 miles per hour**.

Would you like more details or have any questions?

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Here are some related questions to deepen your understanding:
1. How would the result change if Jessica ran at a different speed in the second part?
2. What if Amy took longer than 45 minutes to run the same distance?
3. How do you calculate the average speed when multiple speed intervals are involved?
4. Can you calculate Jessica's average speed for the entire run?
5. How does the total time taken affect the average speed in this kind of problem?

**Tip:** Always ensure units are consistent when solving speed, distance, and time problems, especially converting minutes to hours.

Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.

This problem involves calculating Amy's average speed based on the total distance Jessica runs, using the formulas for distance and average speed. Key concepts include speed, distance, and time, with unit conversion between minutes and hours. Suitable for Grades 7-10.

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