Michael runs a distance of 
5
1
4
 miles in 
45
3
4
 minutes during a race. Which statements correctly represent Michael's race? Choose all that are correct.

	A.	
Michael's average pace was about 0.11 miles per minute.

	B.	
Michael's unit rate of minutes per mile was about 6.9.

	C.	
Michael's unit rate of minutes per mile was about 8.7.

	D.	
Michael's average speed during the race was about 6.9 miles per hour.

	E.	
Michael ran about 8.7 miles in 1 minute.



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.

Michael runs a distance of 5 1/4 miles in 45 3/4 minutes during a race. Which statements correctly represent Michael's race? Choose all that are correct.

A. Michael's average pace was about 0.11 miles per minute.
B. Michael's unit rate of minutes per mile was about 6.9.
C. Michael's unit rate of minutes per mile was about 8.7.
D. Michael's average speed during the race was about 6.9 miles per hour.
E. Michael ran about 8.7 miles in 1 minute.

Solve a real-world problem where Michael runs 5 1/4 miles in 45 3/4 minutes. Learn how to calculate pace, speed, and unit rates with key mathematical concepts and step-by-step solutions. Suitable for Grades 7-9.

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