A piece of land is 2 5/6 miles wide. It is 6 1/2 times as long as it is wide. How long is the piece of land?

To find how long the piece of land is, we need to multiply its width by the factor that represents how much longer it is compared to the width. 

The width is given as \( 2 \frac{5}{6} \) miles, and the land is \( 6 \frac{1}{2} \) times as long as it is wide.

### Step 1: Convert the mixed numbers into improper fractions.
- \( 2 \frac{5}{6} \) = \( \frac{17}{6} \)
- \( 6 \frac{1}{2} \) = \( \frac{13}{2} \)

### Step 2: Multiply the width by the length factor.
\[
\text{Length} = \frac{17}{6} \times \frac{13}{2}
\]
Multiply the numerators and the denominators:
\[
\frac{17 \times 13}{6 \times 2} = \frac{221}{12}
\]

### Step 3: Convert the improper fraction to a mixed number.
\[
\frac{221}{12} = 18 \frac{5}{12}
\]

Thus, the length of the piece of land is **18 \(\frac{5}{12}\)** miles.

Would you like more details on any of these steps or further clarification?

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Here are five related questions to deepen understanding:

1. How would the result change if the width was doubled but the length factor remained the same?
2. What is the perimeter of the land based on the calculated length and width?
3. How would you convert the length from miles to kilometers?
4. Can you calculate the area of the land based on these dimensions?
5. How does multiplying mixed numbers differ from multiplying whole numbers?

**Tip:** When multiplying mixed numbers, it's easier to first convert them to improper fractions.

This problem teaches how to find the length of a piece of land that is 2 5/6 miles wide and 6 1/2 times as long as it is wide. The solution involves converting mixed numbers to improper fractions and multiplying. Suitable for students in Grades 6-8.

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