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In this problem, we need to determine how many flags are required to mark a 7.5-mile racecourse, with one flag placed every 400 yards, including one at the finish line.

The key idea is to convert the total distance from miles to yards, and then divide that by 400 yards to find the number of flags.

Here’s the step-by-step approach based on the provided ratios:

### Given Data:
- Total distance of the racecourse: **7.5 miles**
- A flag is placed every **400 yards**.

We are provided with the following conversion factors:
1. \( 1 \text{ mile} = 5280 \text{ feet} \)
2. \( 1 \text{ yard} = 3 \text{ feet} \)
3. \( 1 \text{ flag} = 400 \text{ yards} \)

### Step-by-Step Solution:
1. Start with the total distance in miles: \( 7.5 \text{ miles} \).
2. Use the conversion factor \( 1 \text{ mile} = 5280 \text{ feet} \) to convert miles to feet:
   \[
   7.5 \text{ miles} \times \frac{5280 \text{ feet}}{1 \text{ mile}} = 39600 \text{ feet}
   \]
3. Use the conversion factor \( 1 \text{ yard} = 3 \text{ feet} \) to convert feet to yards:
   \[
   39600 \text{ feet} \times \frac{1 \text{ yard}}{3 \text{ feet}} = 13200 \text{ yards}
   \]
4. Now, divide the total distance in yards by 400 yards (distance between flags):
   \[
   \frac{13200 \text{ yards}}{400 \text{ yards}} = 33 \text{ flags}
   \]

Thus, **33 flags** are needed to mark the course.

Would you like further details or have any questions?

### Five Related Questions:
1. How would the answer change if the race distance was 10 miles instead of 7.5 miles?
2. How many flags would be needed if the officials placed a flag every 300 yards?
3. What is the equivalent of 7.5 miles in kilometers?
4. If the distance between flags was increased to 500 yards, how many flags would be required?
5. How would you calculate the number of flags if the race distance was given in kilometers?

### Tip:
Always convert all units to the same system (like converting miles to yards or feet) before performing calculations in multi-step unit conversion problems.

A runner's racecourse has a total distance of 7.5 miles. Race officials want to mark the course every 400 yards with a flag, including one at the finish line. How many flags are needed?

Learn how to calculate the number of flags needed for a 7.5-mile racecourse, with flags placed every 400 yards. This problem involves unit conversions and simple division. Suitable for students in Grades 6-8.

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