If the scale of two maps are (a;1:100,000 and b;1:400,000) what is the ground distance if the distance between two towns on the maps is 10cm?

Answer Details

To find the ground distance between two towns given the scale of two maps, we can use the concept of map scale. Map scale is the ratio of the distance on a map to the corresponding distance on the ground. For map scale a of 1:100,000, it means that one unit on the map represents 100,000 units on the ground. For map scale b of 1:400,000, it means that one unit on the map represents 400,000 units on the ground. Given the distance of 10cm between the two towns on the maps, we need to convert it to the actual ground distance. For map a, 1cm on the map represents 100,000cm on the ground. Therefore, 10cm on the map represents 10 x 100,000cm = 1,000,000cm = 10km on the ground. For map b, 1cm on the map represents 400,000cm on the ground. Therefore, 10cm on the map represents 10 x 400,000cm = 4,000,000cm = 40km on the ground. So the correct answer is 10km and 40km.