On a​ map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map. What is the actual distance between the​ houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is more helpful for solving the​ problem? Explain.

Question

The actual distance between the houses is __miles.

Answer 1

To find the actual distance between the two houses that are 3.5 inches apart on the map, we can use the scale given: 1 inch equals 9.2 miles.

Step 1: Calculate the actual distance

To calculate the actual distance represented by 3.5 inches, we multiply the number of inches by the miles per inch:

\[ \text{Actual distance} = \text{Distance on map} \times \text{Scale} \]

\[ \text{Actual distance} = 3.5 \text{ inches} \times 9.2 \text{ miles/inch} \]

\[ \text{Actual distance} = 32.2 \text{ miles} \]

Step 2: Represent the scale with two different ratios

1. Ratio of inches to miles: This represents the scale of the map.

   \[ \text{Ratio} = \frac{1 \text{ inch}}{9.2 \text{ miles}} = \frac{1}{9.2} \]

2. Ratio of miles to inches: This is the inverse of the first ratio.

   \[ \text{Ratio} = \frac{9.2 \text{ miles}}{1 \text{ inch}} = \frac{9.2}{1} \]

Step 3: Determine which ratio is more helpful

The ratio \( \frac{1 \text{ inch}}{9.2 \text{ miles}} \) is more helpful for solving the problem because it directly tells us how many miles correspond to each inch on the map. This makes it straightforward to convert the distance on the map (in inches) to the actual distance (in miles) using simple multiplication.

Final answer

The actual distance between the houses is \( 32.2 \text{ miles}. \)