Final answer:
To find the actual distance between two cities on a map with a scale of 2cm = 5km and a map distance of 31.2cm, set up a proportion and solve it to get an actual distance of 78 kilometers.
Step-by-step explanation:
To determine the actual distance between two cities on a map with a given scale, you can set up a proportion based on the scale and then use cross-multiplication to find the distance.
Given the scale that 2cm = 5km, and the distance between the cities on the map is 31.2cm, we can set up the following proportion to find the actual distance:
2cm / 5km = 31.2cm / x km,
where x represents the actual distance in kilometers.
Now, cross-multiply to solve for x:
2cm * x km = 5km * 31.2cm,
x = (5km * 31.2cm) / 2cm,
x = 78km.
Therefore, the actual distance between the two cities is 78 kilometers.