Explanation:
To find the distance between the two cities on a map with a scale of 1:3,000,000, you can use the concept of proportional scaling.
First, determine the actual distance between the two cities using the scale of 1:100,000. On the 1:100,000 scale map, the distance is 12 cm.
Now, you want to find the equivalent distance on a map with a scale of 1:3,000,000. Let's call this distance "x."
Set up a proportion using the scales:
(Distance on the 1:100,000 scale map) / (Distance on the 1:3,000,000 scale map) = (Scale of the 1:100,000 map) / (Scale of the 1:3,000,000 map)
Plug in the known values:
(12 cm) / x = (1/100,000) / (1/3,000,000)
Simplify and solve for x:
(12 cm) / x = (3,000,000) / 100,000
(12 cm) / x = 30
Now, isolate x:
x = 12 cm / 30
x = 0.4 cm
So, on a map with a scale of 1:3,000,000, the distance between these two cities would be approximately 0.4 cm.