Dale bought a map of his city. It uses a scale from 1 inch to 8 miles. Sales house and school are 1 1/2 inches apart on the map. How far apart would his house and school be?
The correct answer and explanation is:
To determine the actual distance between Dale’s house and school, we use the map scale and the distance on the map:
Map Scale: 1 inch = 8 miles
Map Distance: 1 1/2 inches
Step-by-Step Calculation:
1 1/2 inches = 32\frac{3}{2} inches
Multiply the number of inches on the map by the number of miles per inch: 32×8=242=12 miles\frac{3}{2} \times 8 = \frac{24}{2} = 12 \text{ miles}
✅ Correct Answer: 12 miles
Explanation (300 Words):
Understanding how to convert map distances to real-world distances is essential when interpreting scaled diagrams. In this problem, Dale bought a city map where 1 inch represents 8 miles in real life. This means that every inch on the map corresponds to an actual 8-mile stretch in the city.
Now, Dale observed that his house and school are 1 1/2 inches apart on the map. To work with this measurement more easily in calculations, we first convert the mixed number to a fraction. 1 1/2 inches is equivalent to 3/2 inches.
Next, we apply the scale to determine the real-world distance. Since 1 inch equals 8 miles, we multiply the map distance by 8: 32 inches×8 miles per inch=242=12 miles\frac{3}{2} \text{ inches} \times 8 \text{ miles per inch} = \frac{24}{2} = 12 \text{ miles}
So, in reality, Dale’s house and his school are 12 miles apart.
This method of using ratios or proportions is common in map reading, blueprint interpretation, and even model-making. The scale provides a simplified, smaller version of something much larger. As long as the scale remains consistent, you can measure any distance on the map and calculate its real-world counterpart by multiplying it by the scale factor.
Understanding map scales is not only helpful in geography and navigation but also develops proportional reasoning, which is a key math skill used in many professions, including architecture, engineering, and nursing (e.g., dosage calculations based on ratios).