1. Along a highway there is a post every 1/4 mile. Which of the following is closest to the distance, in miles, between the 17th post and the 82nd post?
Answer: C
The distance between the 17th post and the 82nd post is 16 miles.
To find the distance between the 17th post and the 82nd post, we calculate the number of posts between them, which is 82 - 17 = 65 posts. Since each post is spaced 1/4 mile apart, the total distance is 65 posts * 1/4 mile/post = 16.25 miles, which is closest to 16 miles.
A) 15 1/4
This option represents 15.25 miles, which is less than the calculated distance of 16.25 miles. Therefore, it is incorrect because it underestimates the distance between the two posts.
B) 16
This option indicates a distance of exactly 16 miles. While it is close to the calculated distance of 16.25 miles, it does not accurately represent the total distance between the 17th and 82nd posts, making it slightly incorrect.
C) 16
This option is the correct answer as it is the value that is closest to the calculated distance of 16.25 miles. Although it is not exact, it is the best approximation among the provided choices.
D) 16 1/4
This option represents a distance of 16.25 miles, which is the exact calculated distance between the two posts. However, it is not the closest match; therefore, it is not selected as the correct answer.
E) 16 1/2
This option represents a distance of 16.5 miles, which is greater than the calculated distance of 16.25 miles. Thus, it is incorrect as it overestimates the distance between the posts.
Conclusion
The correct answer, 16 miles, is the closest approximation to the actual distance of 16.25 miles between the 17th and 82nd posts. Options A, B, D, and E either underestimate or overestimate this distance, making them less accurate than option C. Therefore, option C is the most appropriate choice based on the given calculations.