Question

On a map, 1.5 cm represents 50 miles. If the distance between the two cities on the map is 6 cm, how many miles separate the cities? Please explain the steps to solve this problem.

Answer 1

To find the number of miles that separate the cities, we can set up a proportion using the scale given on the map. By cross-multiplying and dividing, we can find the actual distance between the cities.

Step-by-step explanation:

To solve this problem, we need to set up a proportion using the given scale. On the map, 1.5 cm represents 50 miles, so we can write this as 1.5 cm/50 miles.

Now, we can set up the proportion using the distance on the map and the unknown distance between the cities: 1.5 cm/50 miles = 6 cm/x miles.

To solve for x, we can cross-multiply and then divide: 1.5 cm * x miles = 6 cm * 50 miles. Simplifying this gives us x miles = 6 cm * 50 miles / 1.5 cm.

Finally, we can calculate the actual distance in miles by evaluating the expression: x miles = 6 cm * 50 miles / 1.5 cm = 200 miles. Therefore, the cities are 200 miles apart.