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Question

Part 1
Challenge  A map of a highway has a scale of 2 inchesequals45 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the​ highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new​ map?
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Part 1
The rest stops on the new map are
  
enter your response here ​inch(es) apart.

Answer 1

To solve this problem, we first need to determine the total length of the highway based on the original map.

1. Calculate the total length of the highway: The scale of the original map is 2 inches = 45 miles. Therefore, for 6 inches on the map:

   \[ \text{Length of the highway} = \left( \frac{45 \text{ miles}}{2 \text{ inches}} \right) \times 6 \text{ inches} = \frac{45 \times 6}{2} = 135 \text{ miles} \]

2. Determine the distances between the rest stops: There are 11 rest stops equally spaced along the highway, including one at each end. This means there are 10 intervals between the 11 rest stops.

   \[ \text{Distance between rest stops} = \frac{135 \text{ miles}}{10} = 13.5 \text{ miles} \]

3. Convert this distance to the new map scale: The new map has a scale of 1 inch = 30 miles. To find out how many inches 13.5 miles is on the new map, we can set up a proportion:

   \[ \text{Distance in inches} = \frac{13.5 \text{ miles}}{30 \text{ miles/inch}} = \frac{13.5}{30} = 0.45 \text{ inches} \]

Thus, the rest stops on the new map are 0.45 inches apart.

Therefore, your response will be: The rest stops on the new map are 0.45 inches apart.