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.

Question

If the length on the map represents the actual distance, what is the scale factor of the map?

Answer 1

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.