A map of a nature park has a scale of 2 inches to 1.5 miles. There are two trails that are 8 inches apart on the map. What is the actual distance between the two trails?
Understand the Problem
The question describes a map with a given scale and asks to determine the actual distance between two trails that are a certain distance apart on the map. We need to use the scale to convert the map distance to the real-world distance.
Answer
18. 5 miles ```
Answer for screen readers
- 5 miles
Steps to Solve
- Understand the scale
The map scale is given as 1 inch = 5 miles. This means every inch on the map corresponds to 5 miles in the real world.
- Identify the map distance
The two trails are 3.5 inches apart on the map.
- Convert map distance to actual distance
To find the actual distance, multiply the map distance (in inches) by the scale factor (miles per inch): $$ \text{Actual distance} = \text{Map distance} \times \text{Scale} $$ $$ \text{Actual distance} = 3.5 \text{ inches} \times 5 \frac{\text{miles}}{\text{inch}} $$
- Calculate the actual distance
$$ \text{Actual distance} = 3.5 \times 5 \text{ miles} $$ $$ \text{Actual distance} = 17.5 \text{ miles} $$
- 5 miles
More Information
The concept of map scales is crucial in geography, cartography, and navigation. It allows us to represent large areas in a manageable format and accurately determine distances and sizes.
Tips
A common mistake is to divide the map distance by the scale instead of multiplying. Remembering that the actual distance should be larger than the map distance can help avoid this error. Also, forgetting to include the units (miles) in the final answer is a frequent oversight.
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