Finding Scale Distance From Actual Distance

In this problem, we’re told that 2 towns are 15 miles apart and were asked how many inches apart they’ll be drawn on a map that is drawn at a 1 to 10,000 scale. To figure out how many inches apart they’ll be, we need to convert their actual distance apart into inches, and then divide it down to the map scale. We have 15 miles.

We’re going to multiply that by 5,280 feet per 1 mile. The miles will cancel, and we’re left with 15 times 5,280 feet. 5,280 times 15. 5 times zero is zero. 5 times 8 is 40. 5 times 2 is 10 plus 4 is 14. 5 times 5 is 25 plus 1 is 26. 1 times zero, 1 times 8, 1 times 2, and 1 times 5. We’ll add these up and we get 79,200. 15 miles is 79,200 feet.

Now, we need to convert our feet to inches. To do that, we’ll multiply 79,200 feet times 12 inches per 1 foot. The feet cancel, and we have 79,200 times 12. We’ll come over here and do this multiplication. 2 times 2 is 4. 2 times 9 is 18. 2 times 7 is 14 plus 1 is 15. 1 times zero, 1 times 2, 1 times 9, and 1 times 7. We’ll add these up, and we get 950,400 inches.

Now we know the number of inches in 15 miles, but we need to reduce this to a 1 to 10,000 scale. We’re going to divide our number of inches by 10,000. 950,400 divided by 10,000- there ares four zeroes, so we’re going to move our decimal point four places to the left (1, 2, 3, 4). It’s 95.04 inches. That’s how far apart those two towns will be drawn on the map.