Reasoning On a​ map, 1 inch equals 9.4 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

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Part 1
The actual distance between the houses is
  
enter your response here miles.

Answer 1

To find the actual distance between the two houses shown on the map, we can use the scale provided: 1 inch equals 9.4 miles.

Step 1: Calculate the Actual Distance

Given that the distance on the map between the two houses is 3.5 inches, we can calculate the actual distance using the scale:

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

Substituting the values:

\[ \text{Actual Distance} = 3.5 \text{ inches} \times 9.4 \text{ miles per inch} \]

\[ \text{Actual Distance} = 32.9 \text{ miles} \]

Part 1 Answer:

The actual distance between the houses is 32.9 miles.

Part 2: Representing the Scale with Ratios

We can represent the scale (1 inch = 9.4 miles) in two different ratios:

1. Ratio of Map Distance to Actual Distance: \[ \text{Map Distance} : \text{Actual Distance} = 1 \text{ inch} : 9.4 \text{ miles} \]

2. Ratio of Actual Distance to Map Distance: \[ \text{Actual Distance} : \text{Map Distance} = 9.4 \text{ miles} : 1 \text{ inch} \]

More Helpful Ratio

For solving this specific problem, the first ratio (Map Distance : Actual Distance) is more helpful. This is because it allows us to directly convert the distance shown on the map (in inches) to the actual distance (in miles) without needing to invert the ratio.

In summary, the actual distance between the houses is 32.9 miles, and the ratio of map distance to actual distance (1 inch : 9.4 miles) facilitates the calculation.