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 scale of 2 inches representing 1.5 miles. Two trails on the map are 8 inches apart. The problem asks to calculate the actual distance between the two trails in miles, based on the given scale.
Answer
6
Answer for screen readers
6
Steps to Solve
- Find the scaling factor
Divide the map distance between the two trails (8 inches) by the given scale distance (2 inches) to find how many times larger the trails are on the map compared to the given scale.
$ \text{scaling factor} = \frac{8 \text{ inches}}{2 \text{ inches}} = 4 $
- Calculate the actual distance
Multiply the scaling factor calculated in the previous step by the actual distance given in the scale (1.5 miles) to find the actual distance between the trails.
$ \text{actual distance} = 4 \times 1.5 \text{ miles} = 6 \text{ miles} $
6
More Information
The calculated distance represents the real-world distance between the two trails in the nature park.
Tips
A common mistake is to set up the proportion incorrectly, for example, by inverting the ratio or not keeping the units consistent. Another mistake would be to add instead of multiply
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