On a map, two cities are 634 inches apart. The scale of the map is 14 inch =10 miles. What is the actual distance between the two cities?
(634/10) * 14 inches
To find the actual distance between the two cities, we need to use the scale of the map. The given scale is 14 inches = 10 miles.
First, let's determine the ratio between inches and miles. We divide the numerator and denominator of the scale by 14 to simplify it: 14/14 inches = 1 inch, and 10/14 miles ≈ 0.714 miles.
Now, let's use this ratio to calculate the actual distance between the two cities. Given that they are 634 inches apart on the map, we can set up the following proportion:
1 inch / x miles = 634 inches / actual distance
Cross-multiplying, we get:
634 inches * 1 mile = x miles * actual distance
Now, let’s calculate the actual distance:
634 inches * 1 mile / 1 inch = x miles * actual distance
634 miles = x miles * actual distance
To isolate the actual distance, we divide both sides of the equation by x miles:
634 miles / x miles = actual distance
The distance in miles is a constant, so this simplifies to:
634 = actual distance
Therefore, the actual distance between the two cities is 634 miles.