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?

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.