a map of Vicksburg Mississippi has a scale of 1 mile to the inch. The map has been reduced so that 5 inches on the original map appears as 1.5 inches on the reduced map. The distance between two points on the reduced map is 1.75 inches. What is the actual distance in miles?
2.625
To find the actual distance between two points on the reduced map, we need to convert the reduced map distance to the corresponding distance on the original map, and then convert it to miles using the scale provided.
Let's start by finding the corresponding distance on the original map. We know that 5 inches on the original map is represented as 1.5 inches on the reduced map.
So, to find the corresponding original map distance, we can set up a proportion:
5 inches (original map) / 1.5 inches (reduced map) = x (actual distance) / 1.75 inches (reduced map distance)
Cross-multiplying, we get:
5 inches (original map) * 1.75 inches (reduced map distance) = 1.5 inches (reduced map) * x (actual distance)
8.75 inches (original map distance) = 1.5 inches (reduced map) * x (actual distance)
Now, let's convert this original map distance to miles using the given scale of 1 mile to the inch. We can set up another proportion:
1 mile / 1 inch = y (actual distance in miles) / 8.75 inches (original map distance)
Cross-multiplying, we get:
1 mile * 8.75 inches (original map distance) = 1 inch * y (actual distance in miles)
8.75 miles = y (actual distance in miles)
Therefore, the actual distance between the two points on the original map is 8.75 miles.