Final answer:
Mapping problems use scale ratios to convert map distances to actual distances. By setting up and solving simple proportions based on the given scale, one can determine the map or real-world distance correlated to each other. This method applies to any specified scale and measurement combination.
Step-by-step explanation:
To solve mapping problems like these, it’s necessary to use the concept of a scale ratio, where the map distance (in inches) is related to the actual distance (in miles). For each map scale, we set up a proportion and solve for the missing distance. Here’s how that works:
Example Problems:
Using the scale 1 inch=5.5 miles, figure out the number of inches needed to map each number of miles. To find the scale measurement for 16.5 miles, for example, the proportion is 1 inch/5.5 miles = x inches/16.5 miles.
After cross-multiplication, x would be the number of inches on the map that would represent 16.5 miles.
These step-by-step conversions are applicable to each of the miles stated to find the corresponding inch representation on the map.
In the case of scale 0.5 inches=100 miles, we want to determine the actual miles represented by each scale measurement.
For a scale measurement of 8.1 inches, the proportion is 0.5 inches/100 miles = 8.1 inches/x miles. Solving this will give us the actual distance in miles for the 8.1 inches on the map.