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

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
Transcript text: The scale for a map is 20 miles $=\frac{1}{2}$ inch. The distance between two towns on the map is $3 \frac{3}{4}$ inches. What is the actual distance between these towns? (A) $\mathbf{1 5 0}$ miles (B) 38 miles (C) 75 miles (D) 135 miles
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Solution

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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.

Step 1: Understand the Scale

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.

Step 2: Convert Map Distance to Half Inches

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: \[ 3.75 \text{ inches} = \frac{3.75}{0.5} = 7.5 \text{ half inches} \]

Step 3: Calculate the Actual Distance

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

Final Answer

The actual distance between the towns is \(\boxed{150 \text{ miles}}\).

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