The scale on a map is drawn so that 4.5
inches corresponds to an actual distance of 425
miles. If two cities are 11.25
inches apart on the map, how many miles apart are they? (Round to the nearest tenth)

To solve this problem, we need to use the concept of ratios, based on the given scale of the map.

The scale given is:
- 4.5 inches corresponds to 425 miles.

We need to find the actual distance corresponding to 11.25 inches on the map. Let \( x \) be the actual distance in miles.

We can set up a proportion:

\[
\frac{4.5 \text{ inches}}{425 \text{ miles}} = \frac{11.25 \text{ inches}}{x \text{ miles}}
\]

Now, solve for \( x \):

\[
x = \frac{11.25 \times 425}{4.5}
\]

Calculating this:

\[
x = \frac{4781.25}{4.5} \approx 1062.5 \text{ miles}
\]

So, the two cities are approximately **1062.5 miles** apart.

Would you like further details or have any questions about this solution?

Here are five related questions for practice:
1. If the scale was 3 inches to 200 miles, how far would 7.5 inches represent?
2. What would be the scale if 6 inches on the map corresponded to 600 miles in reality?
3. How many miles would 15 inches on the map represent if the scale was 5 inches to 300 miles?
4. If the actual distance between two cities is 850 miles, how far apart would they be on the map if the scale is 1 inch to 150 miles?
5. If 2.5 inches on the map corresponds to 275 miles, how many miles would 12 inches represent?

**Tip:** Always double-check your setup when working with proportions to ensure you're relating the correct units to each other.

Learn how to calculate the actual distance between cities on a map using scale conversion. This problem involves understanding proportions and ratios in map scales. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation