Question

1. A map shows the distance between Dallas and Houston as 3 inches. The actual distance is 240 miles. If there are 63,360 inches in a mile, find the ratio of the distance on the map to the actual distance between Dallas and Houston.

Answer 1

To find the ratio of the distance on the map to the actual distance between Dallas and Houston, we need to find the length of one inch on the map first.

Since the map shows the distance between Dallas and Houston as 3 inches and the actual distance is 240 miles, we can set up a proportion:

3 inches / 240 miles = 1 inch / x miles

To find the length of one inch on the map, we can cross-multiply and solve for x:

3 inches * x miles = 1 inch * 240 miles

3x = 240

x = 240 / 3

x = 80

Therefore, the length of one inch on the map represents 80 miles.

Now, to find the ratio of the distance on the map to the actual distance between Dallas and Houston, we divide the distance on the map (3 inches) by the actual distance (240 miles) and multiply it by the conversion factor from inches to miles (63,360 inches/mile):

(3 inches / 240 miles) * (63,360 inches/mile) = 793.6

Therefore, the ratio of the distance on the map to the actual distance between Dallas and Houston is approximately 793.6:1.