Final answer:
To find the length of the tunnel on the map, we use a proportion based on the scale given: 1 inch equates to 60 miles. Solving the proportion, we find that the 460-mile tunnel is represented by approximately 7.67 inches on the map.
Step-by-step explanation:
To determine the length of the tunnel shown on the map, we will use the given scale, which states that 1 inch on the map represents 60 miles in reality.
To find the length on the map, we can set up a proportion where the actual distance (460 miles) is proportional to the length of the tunnel on the map (in inches):
\(\frac{1\text{ inch}}{60\text{ miles}} = \frac{x\text{ inches}}{460\text{ miles}}\)
Now, we solve for \(x\) by cross-multiplication:
\(60\text{ miles} \times x\text{ inches} = 1\text{ inch} \times 460\text{ miles}\)
\(60x = 460\)
\(x = \frac{460}{60}\)
\(x = 7.67\)
The length of the tunnel shown on the map would therefore be approximately 7.67 inches.