The National Park Service is building a 16-mile hiking trail. They will post a sign every (1)/(8) mile along the trail, including one at the end. There will not be a sign posted at the beginning of the trail. How many signs will they post along the trail? 24 88 128
The correct answer and explanation is:
Correct Answer: 128 signs
Explanation:
The National Park Service is building a 16-mile hiking trail and will place signs every 18\frac{1}{8} mile, but not at the beginning. We need to determine the total number of signs they will post.
Step 1: Determine the Number of Sign Locations
Each sign is placed at intervals of 18\frac{1}{8} mile, so we calculate how many such intervals fit into 16 miles: 1618=16×8=128\frac{16}{\frac{1}{8}} = 16 \times 8 = 128
This calculation tells us that there are 128 positions where a sign will be posted.
Step 2: Check the Conditions of the Problem
- Signs are not placed at the beginning (0 miles).
- Signs are placed every 18\frac{1}{8} mile up to the end (16 miles).
- The final sign is placed at the end (16 miles).
Thus, the total number of signs is 128.
Why the Other Answers Are Incorrect
- 24 signs: This would be correct if signs were placed every 23\frac{2}{3} mile (since 16÷23=2416 \div \frac{2}{3} = 24), but that is not the given interval.
- 88 signs: This does not correspond to any logical fraction of 16 miles.
Thus, the correct answer is 128 signs.
Image Representation
Now, I will generate an image illustrating the 16-mile trail with signs placed at every 18\frac{1}{8} mile.
Here is an illustrated representation of the 16-mile hiking trail with signs placed every 18\frac{1}{8} mile. The image visually depicts the concept of evenly spaced markers along a scenic path. Let me know if you need any modifications!C
