To solve this problem using proportions, we'll compare the map scale to the actual distance.

Step 1: Set up the proportion

The map scale tells us that 0.5 inches on the map corresponds to 1 mile in reality. The problem states that the distance between the two museums on the map is 2.6 inches. We can set up a proportion to solve for the actual distance (denoted as $x$) in miles:

$\frac{0.5 \text{ inches}}{1 \text{ mile}} = \frac{2.6 \text{ inches}}{x \text{ miles}}$

Step 2: Solve the proportion

Cross-multiply to solve for $x$:

$0.5 \cdot x = 1 \cdot 2.6$

$0.5x = 2.6$

Now, divide both sides by 0.5 to find $x$:

$x = \frac{2.6}{0.5}$

$x = 5.2 \text{ miles}$

Conclusion:

The actual distance between the two museums is approximately 5.2 miles.

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Would you like further details on this, or do you have any questions?

Here are some related questions you might find useful:

1. How would the distance change if the scale was 0.25 inches to 1 mile?
2. What if the museums were 4 inches apart? What would be the actual distance?
3. How does map scale factor influence the representation of actual distances?
4. What are the steps for converting inches to miles on a different map scale?
5. How would you calculate the distance if the scale was reversed, i.e., 1 inch equals 2 miles?

Tip: Always double-check your units when solving proportion problems to ensure accurate calculations.