The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334

Question

inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 514
inches apart on the map. The scale on the map is 12
inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville? Enter your answer in the box.

mi

Answer 1

To find the actual distance the Patel family will travel, we first need to convert the distances on the map into actual miles using the provided scale: 12 inches equals 4 miles.

Step 1: Calculate the total distance on the map.

The distances on the map are:

• Smithville to Jonesville = 334 inches
• Jonesville to Clarksville = 514 inches

Total distance on the map = \( 334 + 514 = 848 \) inches.

Step 2: Calculate the actual distance based on the scale.

From the scale, we know: \[ 12 \text{ inches} = 4 \text{ miles} \]

To find out how many miles correspond to 1 inch, we can calculate: \[ 1 \text{ inch} = \frac{4 \text{ miles}}{12 \text{ inches}} = \frac{1}{3} \text{ miles per inch} \]

Step 3: Convert the total distance from inches to miles.

Now, we convert the total distance of 848 inches to miles: \[ \text{Actual distance} = 848 \text{ inches} \times \frac{1}{3} \text{ miles per inch} = \frac{848}{3} \text{ miles} \approx 282.67 \text{ miles} \]

The actual distance the Patel family will travel by the time they reach Clarksville is approximately 282.67 miles.