Let's solve this step-by-step to determine which statements are correct.

Step 1: Convert the mixed numbers to improper fractions

Michael's distance is given as $5 \frac{1}{4}$ miles, and his time is $45 \frac{3}{4}$ minutes.

• $5 \frac{1}{4} = \frac{21}{4}$ miles
• $45 \frac{3}{4} = \frac{183}{4}$ minutes

Step 2: Find the average pace in miles per minute

To find Michael's average pace, we divide the total distance by the total time:

$\text{Pace} = \frac{\frac{21}{4}}{\frac{183}{4}} = \frac{21}{183} \approx 0.1148 \, \text{miles per minute}$

So, his average pace is approximately $0.11$ miles per minute, which means Statement A is correct.

Step 3: Find the unit rate of minutes per mile

To find the number of minutes per mile (his unit rate), we divide the total time by the total distance:

$\text{Minutes per mile} = \frac{\frac{183}{4}}{\frac{21}{4}} = \frac{183}{21} = 8.714 \, \text{minutes per mile}$

So, his unit rate is approximately $8.7$ minutes per mile, which means Statement C is correct. Since Statement B says $6.9$ minutes per mile, Statement B is incorrect.

Step 4: Find Michael's speed in miles per hour

To find Michael's speed in miles per hour, we need to convert his time into hours. $45 \frac{3}{4}$ minutes is $45.75$ minutes, which is $\frac{45.75}{60} = 0.7625$ hours.

Now, divide the total distance by the time in hours:

$\text{Speed} = \frac{5.25}{0.7625} \approx 6.88 \, \text{miles per hour}$

So, his average speed is about $6.9$ miles per hour, which means Statement D is correct.

Step 5: Analyze Statement E

Statement E says that Michael ran about $8.7$ miles in $1$ minute. This is incorrect because he actually runs about $0.11$ miles per minute (as seen in Step 2), so Statement E is false.

Final Answers:

• A. Correct
• B. Incorrect
• C. Correct
• D. Correct
• E. Incorrect

Would you like more details or have any questions?

Here are five related questions:

1. How do we convert mixed numbers into improper fractions?
2. What is the formula for calculating speed in miles per hour?
3. How can you verify your answers when working with unit rates?
4. Why is it useful to find the pace in both miles per minute and minutes per mile?
5. How does the time conversion affect speed calculations?

Tip: Always double-check your conversions between units (like minutes to hours) to ensure accuracy in speed or pace calculations.