Final answer:
Map scales express the ratio between distances on a map and the corresponding distances on the ground. To find the real-world distance or map distance, you can set up a proportion using the given scale. Calculating these proportions for the provided examples shows how map measures translate to actual distances.
Step-by-step explanation:
Understanding Map Scales and Proportions
When working with map scales, it's important to understand the concept of proportionality. This means that distances on a map are in a constant ratio to the actual distances they represent on the ground. Here, we will solve a series of problems that involve calculating distances using given map scales.
- For 16.5 miles, we use the scale 1 inch=5.5 miles. The proportion is 1 inch / 5.5 miles = x inches / 16.5 miles. Solving for x gives us 3 inches.
- Using the same process, 11 miles on the map would be represented by 2 inches.
- For 27.5 miles, the representation on the map is 5 inches.
- The distance of 8.25 miles corresponds to 1.5 inches on the map.
- A map distance for 33 miles would be 6 inches.
- Calculating for 60.5 miles gives us a map distance of 11 inches.
- 13.75 miles is equivalent to 2.5 inches on the map.
For the second set of problems, we use the scale 0.5 inches=100 miles:
- With a map measurement of 8.1 inches, the actual miles represented are 1620 miles.
- A measurement of 2 inches on the map corresponds to 400 miles in reality.
- Finally, 3 inches on the map scale translates to 600 actual miles.
In the example of the distance from John's house to Mike's house, the map shows 4.5 inches using the scale 1.5 inches=2 miles. This means the actual distance is 6 miles. To get the distance in feet, we multiply by 5280 (the number of feet in a mile), which gives us 31680 feet.