On a map, two cities are four and one-fourth inches apart. The scale of the map is one-half inch = three miles. What is the actual distance between the towns?

3/1.5 = x/4.25

Solve for x.

To find the actual distance between the two cities, we can use the scale given on the map.

According to the scale, one-half inch on the map represents three miles in real life.

First, let's calculate the distance on the map. The cities are four and one-fourth inches apart. To convert this to a fraction, we have 4 + (1/4) inches. Multiplying the whole number by the denominator and adding the numerator, we get 4*4 + 1 = 17/4 inches.

Now, we can use the scale to convert inches on the map to miles in real life. Since 1/2 inch on the map represents 3 miles, we need to set up a proportion:

(17/4) inches / (1/2) inch = x miles / 3 miles

To simplify the proportion, cross-multiply:

(17/4) * (2/1) = x * (3/1)

34/4 = 3x

Now, divide both sides by 3:

34/4 / 3 = x

17/6 = x

Therefore, the actual distance between the two cities is 17/6 miles.