Challenge A map of a highway has a scale of 2 inchesequals45 miles. The length of the highway on the map is 8 inches. There are 17 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?

Question

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Part 1
The rest stops on the new map are
  
enter your response here ​inch(es) apart.

Answer 1

To find the distance between the rest stops on the new map, we first need to determine the total distance represented by the highway on the original map and the distance each rest stop corresponds to on that highway.

1. Find the total distance of the highway based on the original map scale.
   The scale of the original map is \(2\) inches equals \(45\) miles.
   The length of the highway on the map is \(8\) inches.

   Using the scale to find the total distance in miles: \[ \text{Total distance} = \left(\frac{45 \text{ miles}}{2 \text{ inches}}\right) \times 8 \text{ inches} = 180 \text{ miles} \]

2. Determine the distance between the rest stops on the highway.
   There are \(17\) rest stops, including one at each end, which means there are \(16\) equal spaces between the rest stops.
   To find the distance between each rest stop on the highway: \[ \text{Distance between rest stops} = \frac{180 \text{ miles}}{16} = 11.25 \text{ miles} \]

3. Convert the distance between rest stops to the new map scale.
   The new map scale is \(1\) inch equals \(30\) miles.
   To find out how many inches this distance corresponds to on the new map: \[ \text{Distance on new map} = \frac{11.25 \text{ miles}}{30 \text{ miles per inch}} = 0.375 \text{ inches} \]

Thus, the rest stops on the new map are \(0.375\) inches apart.

Final answer: The rest stops on the new map are 0.375 inches apart.