Sarah is exploring a map to plan a hiking route through a national park. The actual distance between two points on the map is 40 kilometers. On the map, the distance between these two points is represented as 5 centimeters.
If the length on the map represents the actual distance, what is the scale factor of the map?
To find the scale factor of the map, we need to determine the ratio of the length on the map to the actual distance.
Length on the map = 5 centimeters
Actual distance = 40 kilometers
To find the scale factor, we need to convert the actual distance to the same unit as the length on the map. Let's convert kilometers to centimeters.
1 kilometer = 100,000 centimeters
Actual distance = 40 kilometers = 40 * 100,000 centimeters = 4,000,000 centimeters
Now we can find the scale factor:
Scale factor = Length on the map / Actual distance
Scale factor = 5 centimeters / 4,000,000 centimeters
Simplifying the scale factor:
Scale factor = 1 / 800,000
Therefore, the scale factor of the map is 1:800000.