Questions: The scale for a map is 20 miles = 1/2 inch. The distance between two towns on the map is 3 3/4 inches. What is the actual distance between these towns? (A) 150 miles (B) 38 miles (C) 75 miles (D) 135 miles

Solution Steps

To find the actual distance between the towns, we need to use the scale provided. The scale is 20 miles for every \( \frac{1}{2} \) inch. First, convert the map distance from inches to miles using the scale, then calculate the total distance.

The scale of the map is given as \( 20 \) miles for every \( \frac{1}{2} \) inch. This means that each \( \frac{1}{2} \) inch on the map represents \( 20 \) miles in reality.

The distance between the two towns on the map is \( 3 \frac{3}{4} \) inches. Convert this to a fraction: \[ 3 \frac{3}{4} = \frac{15}{4} = 3.75 \text{ inches} \] Now, convert inches to half inches: \[ 3.75 \text{ inches} = \frac{3.75}{0.5} = 7.5 \text{ half inches} \]

Using the scale, calculate the actual distance: \[ \text{Actual distance} = 7.5 \times 20 = 150 \text{ miles} \]

Final Answer