To find out how far apart the rest stops are on the new map, we will first need to determine the total distance of the highway represented on the original map and then use that to find the distance between the rest stops.
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Determine the length of the highway: The map has a scale of 2 inches = 27 miles. Since the length of the highway on the map is 9 inches, we can set up a proportion based on the scale:
\[ \text{Scale Factor} = \frac{27 \text{ miles}}{2 \text{ inches}} \]
To find out the total distance represented by 9 inches:
\[ \text{Distance} = \left( \frac{27 \text{ miles}}{2 \text{ inches}} \right) \times 9 \text{ inches} = \frac{27 \times 9}{2} = \frac{243}{2} = 121.5 \text{ miles} \]
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Calculate the distance between rest stops: There are 7 rest stops equally spaced along the highway, including one at each end. This means there are 6 intervals between the 7 stops. To find the distance between each pair of rest stops, we divide the total distance by the number of intervals:
\[ \text{Distance between rest stops} = \frac{121.5 \text{ miles}}{6} = 20.25 \text{ miles} \]
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Convert the distance between rest stops to the new map's scale: Now we take the new map's scale of 1 inch = 30 miles to convert the distance between rest stops into inches:
\[ \text{Distance in inches} = \frac{20.25 \text{ miles}}{30 \text{ miles/inch}} = 0.675 \text{ inches} \]
Thus, the rest stops on the new map are 0.675 inches apart.