To find out what distance on the map represents 1 mile, we can set up a proportion based on the information provided. We know that:
12 inches on the map represents 45 miles.
To find the number of inches that represent 1 mile, we can set up the following proportion:
\[ \frac{12 \text{ inches}}{45 \text{ miles}} = \frac{x \text{ inches}}{1 \text{ mile}} \]
Now, we can solve for \(x\):
\[ x = \frac{12 \text{ inches}}{45 \text{ miles}} \times 1 \text{ mile} \]
\[ x = \frac{12}{45} \]
Now, let's simplify \(\frac{12}{45}\):
\[ \frac{12}{45} = \frac{4}{15} \]
Therefore, 1 mile on the map represents \(\frac{4}{15}\) inches.
Now we can determine which response corresponds to this fraction.
Calculating \(\frac{4}{15}\) as a decimal gives approximately 0.267, which does not match any of the provided options.
Upon reviewing the options given:
- 25 in.
- \( \frac{2}{5} \) in. (which is 0.4 in.)
- 58 in.
- \( \frac{5}{8} \) in. (which is 0.625 in.)
- 135 in.
- \( 1 \frac{3}{5} \) in. (which is 1.625 in.)
- 212 in.
None of these options match with \( \frac{4}{15} \) (or approximately 0.267 in.).
It appears there might have been a misunderstanding of the problem or a miscommunication in the options provided, as our calculations conclude that 1 mile corresponds to \( \frac{4}{15} \) inches on the map. If you have any additional context or information regarding the answers provided, please let me know!