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The problem asks to write two equations that relate the distance measured in kilometers (denoted as \( x \)) and the same distance measured in miles (denoted as \( y \)) using the given conversion factor: 1 mile = 1.61 kilometers.

To do this, we use the following steps:

1. **From kilometers to miles**:
   Since 1 mile = 1.61 kilometers, if you have \( x \) kilometers, to convert it to miles (\( y \)), you divide the kilometers by 1.61:
   \[
   y = \frac{x}{1.61}
   \]
   This equation relates a distance \( x \) in kilometers to the equivalent distance \( y \) in miles.

2. **From miles to kilometers**:
   Similarly, if you have \( y \) miles, to convert it to kilometers (\( x \)), you multiply the miles by 1.61:
   \[
   x = 1.61y
   \]
   This equation relates a distance \( y \) in miles to the equivalent distance \( x \) in kilometers.

### Final Equations:
- \( y = \frac{x}{1.61} \)
- \( x = 1.61y \)

Let me know if you need further explanation!

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Here are five related questions for further practice:

1. If a car travels 50 kilometers, how many miles did it travel?
2. How many kilometers are equivalent to 75 miles?
3. What is the formula to convert from miles to kilometers?
4. If \( x = 32.2 \) kilometers, find the equivalent distance in miles.
5. How would you set up a proportion to solve for kilometers given miles?

**Tip**: Always double-check your units when converting between kilometers and miles to ensure accuracy.

There are about 1.61 kilometers in 1 mile. Use x to represent a distance measured in kilometers and y to represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles.

Learn how to convert distances between kilometers and miles with two simple equations. Understand the relationship between kilometers and miles using proportional relationships. Suitable for students in Grades 6-8.

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