To determine the distance between each of the 6 evenly spaced markers on the trail that is [tex]\(\frac{9}{10}\)[/tex] of a mile long, let's break down the problem step by step:
1. Understand the Configuration of Markers:
- The trail is [tex]\(\frac{9}{10}\)[/tex] of a mile long.
- We have 6 markers placed evenly along the trail.
2. Determine the Number of Segments:
- When we place 6 markers along a trail, these markers divide the trail into segments.
- The first marker is at the start, and the sixth marker is at the end, so these 6 markers create 5 segments.
- Thus, the trail is divided into 5 equal segments by the markers.
3. Calculate the Distance of Each Segment:
- Since the entire length of the trail is [tex]\(\frac{9}{10}\)[/tex] miles and it is divided into 5 segments, the length of each segment can be found by dividing the total length by the number of segments.
- Formula: [tex]\(\text{Distance between markers} = \frac{\text{Total length of the trail}}{\text{Number of segments}}\)[/tex]
- Applying the values: [tex]\(\text{Distance between markers} = \frac{\frac{9}{10} \text{ miles}}{5}\)[/tex]
4. Simplify the Calculation:
- Perform the division: [tex]\(\text{Distance between markers} = \frac{9}{10} \div 5\)[/tex]
- Simplify the division: [tex]\(\text{Distance between markers} = \frac{9}{10} \times \frac{1}{5}\)[/tex]
- Continue simplifying: [tex]\(\text{Distance between markers} = \frac{9}{10} \times \frac{1}{5} = \frac{9}{50} \text{ miles}\)[/tex]
Thus, the distance between each marker is [tex]\(\frac{9}{50}\)[/tex] miles.
To convert this to a decimal for clarity: [tex]\(\frac{9}{50} = 0.18\)[/tex] miles.
So, the markers are placed 0.18 miles apart.
