Answer :
To solve this problem, let's analyze the provided data and determine which description best matches the provided information about the runners.
First, we calculate the distance each runner covered based on their speed and total time.
1. Garreth:
- Total time: 40 minutes
- Speed: 6.2 mph
- Convert time to hours: [tex]\( \frac{40 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{2}{3} \text{ hours} \)[/tex]
- Distance: [tex]\( 6.2 \text{ mph} \times \frac{2}{3} \text{ hours} = 4.13 \text{ miles} \)[/tex]
2. Elisa:
- Total time: 40 minutes
- Speed: 6.2 mph
- Convert time to hours: [tex]\( \frac{40 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{2}{3} \text{ hours} \)[/tex]
- Distance: [tex]\( 6.2 \text{ mph} \times \frac{2}{3} \text{ hours} = 4.13 \text{ miles} \)[/tex]
3. Luigi:
- Total time: 35 minutes
- Speed: 5.0 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.0 \text{ mph} \times 0.583 \text{ hours} \approx 2.915 \text{ miles} \)[/tex]
4. Jasmine:
- Total time: 35 minutes
- Speed: 5.0 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.0 \text{ mph} \times 0.583 \text{ hours} \approx 2.915 \text{ miles} \)[/tex]
5. Logan:
- Total time: 35 minutes
- Speed: 5.6 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.6 \text{ mph} \times 0.583 \text{ hours} \approx 3.257 \text{ miles} \)[/tex]
Next, compare the distances and evaluate the correct statements.
- Garreth and Elisa ran together: They both ran the same distance (4.13 miles).
- Luigi and Jasmine went the same distance: They both ran the same distance (2.915 miles).
- Logan and Jasmine have the same displacement in the opposite direction: Jasmine went [tex]\( 4.0 \text{ mph} \)[/tex] south and Logan went [tex]\( 4.0 \text{ mph} \)[/tex] north, meaning their displacements are the same in magnitude but opposite in direction.
Thus, the best description based on the given data 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.
First, we calculate the distance each runner covered based on their speed and total time.
1. Garreth:
- Total time: 40 minutes
- Speed: 6.2 mph
- Convert time to hours: [tex]\( \frac{40 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{2}{3} \text{ hours} \)[/tex]
- Distance: [tex]\( 6.2 \text{ mph} \times \frac{2}{3} \text{ hours} = 4.13 \text{ miles} \)[/tex]
2. Elisa:
- Total time: 40 minutes
- Speed: 6.2 mph
- Convert time to hours: [tex]\( \frac{40 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{2}{3} \text{ hours} \)[/tex]
- Distance: [tex]\( 6.2 \text{ mph} \times \frac{2}{3} \text{ hours} = 4.13 \text{ miles} \)[/tex]
3. Luigi:
- Total time: 35 minutes
- Speed: 5.0 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.0 \text{ mph} \times 0.583 \text{ hours} \approx 2.915 \text{ miles} \)[/tex]
4. Jasmine:
- Total time: 35 minutes
- Speed: 5.0 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.0 \text{ mph} \times 0.583 \text{ hours} \approx 2.915 \text{ miles} \)[/tex]
5. Logan:
- Total time: 35 minutes
- Speed: 5.6 mph
- Convert time to hours: [tex]\( \frac{35 \text{ minutes}}{60 \text{ minutes/hour}} \approx 0.583 \text{ hours} \)[/tex]
- Distance: [tex]\( 5.6 \text{ mph} \times 0.583 \text{ hours} \approx 3.257 \text{ miles} \)[/tex]
Next, compare the distances and evaluate the correct statements.
- Garreth and Elisa ran together: They both ran the same distance (4.13 miles).
- Luigi and Jasmine went the same distance: They both ran the same distance (2.915 miles).
- Logan and Jasmine have the same displacement in the opposite direction: Jasmine went [tex]\( 4.0 \text{ mph} \)[/tex] south and Logan went [tex]\( 4.0 \text{ mph} \)[/tex] north, meaning their displacements are the same in magnitude but opposite in direction.
Thus, the best description based on the given data 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.
