Let's analyze the given information and determine which statements best describe the runners.
Step-by-Step Analysis:
1. Time Conversion:
- Garreth: 40 minutes = [tex]\(\frac{40}{60}\)[/tex] hours
- Luigi: 35 minutes = [tex]\(\frac{35}{60}\)[/tex] hours
- Elisa: 40 minutes = [tex]\(\frac{40}{60}\)[/tex] hours
- Jasmine: 35 minutes = [tex]\(\frac{35}{60}\)[/tex] hours
- Logan: 35 minutes = [tex]\(\frac{35}{60}\)[/tex] hours
2. Distance Calculated:
- Garreth: [tex]\(6.2 \, \text{mph} \times \frac{40}{60} \, \text{hours} \)[/tex]
- Luigi: [tex]\(5.0 \, \text{mph} \times \frac{35}{60} \, \text{hours} \)[/tex]
- Elisa: [tex]\(6.2 \, \text{mph} \times \frac{40}{60} \, \text{hours} \ )
- Jasmine: \(5.0 \, \text{mph} \times \frac{35}{60} \, \text{hours} \)[/tex]
- Logan: [tex]\(5.6 \, \text{mph} \times \frac{35}{60} \, \text{hours} \ )
3. Velocity Direction Analysis:
- Garreth: West
- Luigi: East
- Elisa: West
- Jasmine: South
- Logan: North
4. Displacement Calculated:
- Garreth: \(5.5 \, \text{mph (west)} \times \frac{40}{60} \, \text{hours} \)[/tex]
- Luigi: [tex]\(4.3 \, \text{mph (east)} \times \frac{35}{60} \, \text{hours} \)[/tex]
- Elisa: [tex]\(5.5 \, \text{mph (west)} \times \frac{40}{60} \, \text{hours} \)[/tex]
- Jasmine: [tex]\(4.0 \, \text{mph (south)} \times \frac{35}{60} \, \text{hours} \)[/tex]
- Logan: [tex]\(4.0 \, \text{mph (north)} \times \frac{35}{60} \, \text{hours} \)[/tex]
5. Distance and Displacement Comparison:
- Garreth and Elisa:
- Distance and direction are the same (6.2 mph for 40 minutes).
- Displacement is the same (5.5 mph west for 40 minutes).
- Luigi and Jasmine:
- Distance is the same (5.0 mph for 35 minutes).
- Displacement is different due to different directions.
- Logan and Jasmine:
- Distance is different (Logan has a higher speed, thus ran a longer distance in the same time).
- Displacement is the same (4.0 mph but in opposite directions).
- Garreth and Luigi:
- Distance: Garreth ran farther (6.2 mph vs. 5.0 mph for respective times).
- Elisa and Jasmine:
- Distance is different (Elisa ran farther due to higher speed).
- Logan:
- Ran faster than Jasmine (higher speed, thus greater distance for same time).
Conclusion:
- Garreth and Elisa ran the same distance and direction, thus they ran together.
- Logan ran faster than Jasmine.
- Garreth ran farther than Luigi.
- Logan and Jasmine have the same displacement but in opposite directions.
- Luigi and Jasmine went the same distance.
Thus, the correct statement is: Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.
