A map of a highway has a scale of 2 inchesequals39 miles. The length of the highway on the map is 9 inches. There are 7 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?

Accepted Solution

Answer:[tex]0.975\ in[/tex]Step-by-step explanation:step 1Find the  distance of the rest stop in the original map[tex]\frac{9}{6}=1.5\ in[/tex]  Divide by 6 because there are 7 rest stopFind the real distance of the rest stop using proportion[tex]\frac{2}{39}\frac{inches}{miles} =\frac{1.5}{x}\frac{inches}{miles}\\ \\x=39*1.5/2\\ \\x=29.25\ miles[/tex]step 2Find the  distance of the rest stop in the new mapusing proportion[tex]\frac{1}{30}\frac{inches}{miles} =\frac{x}{29.25}\frac{inches}{miles}\\ \\x=29.25/30\\ \\x=0.975\ in[/tex]