Isaiah, a high school student, is also enrolled in a class at the local junior college. The college is 2.6 miles away from the high school, and these two are 1 inch away on a map of the area. What is the map's scale?

Question

Write your answer in simplest form using whole numbers.

inches :
miles

Answer 1

To find the map's scale, we need to set up a ratio between the distance on the map and the actual distance.

The actual distance between the high school and the college is 2.6 miles, and this distance corresponds to 1 inch on the map.

We can express the scale as:

\[ \text{Scale} = \frac{\text{Distance on map}}{\text{Actual distance}} = \frac{1 \text{ inch}}{2.6 \text{ miles}} \]

To simplify this scale to whole numbers, we can eliminate the decimal by multiplying both numbers in the ratio by 10:

\[ 1 \text{ inch} : 2.6 \text{ miles} \implies 10 \text{ inches} : 26 \text{ miles} \]

Now, we simplify the ratio \(10 : 26\) by dividing both numbers by their greatest common divisor, which is 2:

\[ \frac{10}{2} : \frac{26}{2} \implies 5 : 13 \]

Thus, the scale of the map in simplest form is:

\[ \boxed{5 : 13} \]