Question

On a map, the distance between two cities is 14 cm, but the actual distance between the two cities is 49 miles. What is the scale factor of the map?

a. 7 cm: 1 mile
b. 1 cm: 7 miles
c. 7 cm: 2 miles
d. 2 cm: 7 miles

Answer 1

The scale factor of the map is 7 cm : 1 mile.

Step-by-step explanation:

To find the scale factor of the map, we need to compare the distance on the map to the actual distance. In this case, the distance on the map is 14 cm and the actual distance is 49 miles.

To find the scale factor, we can set up a proportion using the ratio of the distances. Since the map distance is in centimeters and the actual distance is in miles, we need to convert the units first: 1 mile = 1.61 km = 161,000 cm.

So the proportion becomes: 14 cm / 161,000 cm = x miles / 49 miles. Solving for x, we get x ≈ 0.000087 miles. This can be rounded to 7 cm : 1 mile, which corresponds to option a.