A map is set to a scale factor of 0.5 in 1 mi . Suppose two museums are 2.6 inches apart on a map , use proportions to solve for the actual distance between them . The actual distance between the museums is approximately miles .

To find the actual distance between the two museums based on the map, we can set up a proportion using the scale factor.

### Given:
- The scale factor is 0.5 inches = 1 mile.
- The distance between the museums on the map is 2.6 inches.

We can set up a proportion as follows:

\[
\frac{\text{Map distance (in inches)}}{\text{Actual distance (in miles)}} = \frac{\text{Scale factor in inches}}{\text{Scale factor in miles}}
\]

Substitute the known values:

\[
\frac{2.6}{x} = \frac{0.5}{1}
\]

Now solve for \(x\), which is the actual distance in miles.

1. Cross multiply:

\[
2.6 \times 1 = 0.5 \times x
\]

\[
2.6 = 0.5x
\]

2. Solve for \(x\):

\[
x = \frac{2.6}{0.5} = 5.2
\]

### Conclusion:
The actual distance between the museums is approximately **5.2 miles**.

Would you like more details or have any questions?

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Here are five questions to expand on this topic:

1. How would the actual distance change if the scale factor were 1 inch = 2 miles?
2. If the map distance was given in centimeters, how would you convert it to inches to use the same scale?
3. How can you verify if the scale factor provided is accurate when comparing two known locations?
4. What is the formula for converting map distances to actual distances for different scales?
5. How do changes in map scale affect the accuracy of long-distance measurements?

**Tip**: Always double-check units when setting up proportions to ensure the correct conversion factors!

A map is set to a scale factor of 0.5 in 1 mi. Suppose two museums are 2.6 inches apart on a map, use proportions to solve for the actual distance between them. The actual distance between the museums is approximately miles.

Learn how to determine the actual distance between two locations on a map using proportions and scale factor calculations. This example shows a scale factor of 0.5 inches to 1 mile and uses a distance of 2.6 inches between two museums, ideal for students in Grades 6-8.

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