On a map, `1/4` inch represents 16 actual miles. Two towns are `2 3/4` inches apart on this map are how many actual miles apart?

Options

A. 11
B. 16
C. 44
D. 176

Answer

To solve the problem, we need to determine how many actual miles correspond to the distance of \(2 \frac{3}{4}\) inches on the map, given that \( \frac{1}{4} \) inch represents 16 actual miles.

### Step-by-Step Solution:

1. **Understand the given scale**:
We know that \( \frac{1}{4} \) inch on the map represents 16 actual miles.

2. **Convert the mixed number to an improper fraction**:
The distance between the two towns is given as \(2 \frac{3}{4}\) inches. We convert this mixed number to an improper fraction:
\[ 2 \frac{3}{4} = \frac{4 \times 2 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ inches} \]

3. **Set up the proportion**:
We need to find out how many actual miles correspond to \( \frac{11}{4} \) inches. Since \( \frac{1}{4} \) inch corresponds to 16 miles, we can express the relationship:
\[ \frac{1}{4} \text{ inch} \rightarrow 16 \text{ miles} \]
Therefore, \( \frac{11}{4} \) inches can be calculated as:
\[ \frac{11}{4} \text{ inches} = 11 \times \left( \text{actual miles per } \frac{1}{4} \text{ inch} \right) \]

4. **Calculate the actual miles**:
Since \( \frac{1}{4} \) inch is 16 miles, we can find the actual miles for \( \frac{11}{4} \) inches:
\[ \text{Actual miles} = 11 \times 16 = 176 \text{ miles} \]

5. **Conclusion**:
Therefore, the two towns that are \(2 \frac{3}{4}\) inches apart on the map are actually 176 miles apart.

### Final Answer:
The two towns are 176 miles apart.