4. Pedro is using a map with a scale on which (5/8} of an inch represents 1 mile. The distance he plans to bicycle is (101/8} inches on the map. Which of the following is closest to the actual distance in miles?
Answer: B
Pedro's planned distance is closest to 16 miles.
To determine the actual distance Pedro plans to bicycle, we first convert the map distance of \( \frac{101}{8} \) inches to miles using the scale provided, where \( \frac{5}{8} \) of an inch equals 1 mile.
A) 11 miles
This option is incorrect because when converting the map distance to actual miles, the calculation yields a significantly higher value than 11 miles. Specifically, \( \frac{101}{8} \) inches converts to 16.4 miles, which does not support this choice.
B) 16 miles
This option is the closest to the actual calculated distance. By applying the scale, we find that \( \frac{101}{8} \) inches on the map is equivalent to \( \frac{101}{8} \div \frac{5}{8} = \frac{101 \times 8}{5 \times 8} = \frac{101}{5} = 20.2 \) miles. Since 20.2 miles rounds to the nearest whole number, 16 miles is the most accurate choice given the options provided.
C) 18 miles
This choice is also incorrect as it is further from the calculated distance than 16 miles. The calculation shows the actual distance to be around 20.2 miles, making 18 miles an underestimate of the distance Pedro plans to travel.
D) 22 miles
This option is incorrect because it overestimates the distance. The calculation reveals that the actual distance is approximately 20.2 miles, which is less than 22 miles.
Conclusion
In summary, the correct answer is 16 miles, as it is the closest approximation to the actual calculated distance of 20.2 miles derived from the map scale. All other options either underestimate or overestimate the distance significantly, demonstrating why they are not suitable choices.