$15$ . Higher Order Thinking A map of a highway has a scale of $2$ inches equals $33$ 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?

Full solution

15

. Higher Order Thinking A map of a highway has a scale of

2

inches equals

33

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?

Calculate total highway length: Calculate the total length of the highway in miles using the original scale. $\newline$ $6$ inches $\times (33$ miles $/ 2$ inches) $= 99$ miles.
Determine number of segments: Determine the number of segments between the rest stops. $\newline$ There are $11$ rest stops, so there are $10$ segments between them.
Calculate segment length: Calculate the length of each segment in miles. $\newline$ $99$ miles / $10$ segments = $9.9$ miles per segment.
Convert segment length: Convert the segment length to the new scale on the map. $9.9 \, \text{miles} \times \left(\frac{1 \, \text{inch}}{30 \, \text{miles}}\right) = 0.33 \, \text{inches per segment}.$