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Sagot :
To determine which statement best describes the runners, we need to analyze the given information about the time, speed, and velocity of each runner. We will use this information to compare distances and displacements.
1. Distance Ran by Each Runner:
- Gareth:
- Time: 40 minutes (which is [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex] hours)
- Speed: 6.2 mph
- Distance: [tex]\(6.2 \, \text{mph} \times \frac{2}{3} \, \text{hours} = \frac{12.4}{3} \approx 4.13 \, \text{miles}\)[/tex]
- Luigi:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 6.0 mph
- Distance: [tex]\(6.0 \, \text{mph} \times 0.583 \, \text{hours} \approx 3.50 \, \text{miles}\)[/tex]
- Elisa:
- Time: 40 minutes (which is [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex] hours)
- Speed: 6.2 mph
- Distance: [tex]\(6.2 \, \text{mph} \times \frac{2}{3} \, \text{hours} = \frac{12.4}{3} \approx 4.13 \, \text{miles}\)[/tex]
- Jasmine:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 5.0 mph
- Distance: [tex]\(5.0 \, \text{mph} \times 0.583 \, \text{hours} \approx 2.92 \, \text{miles}\)[/tex]
- Logan:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 5.6 mph
- Distance: [tex]\(5.6 \, \text{mph} \times 0.583 \, \text{hours} \approx 3.26 \, \text{miles}\)[/tex]
2. Displacements:
- Garreth and Elisa: Both ran west at speeds resulting in the same distance of approximately 4.13 miles, but their displacement is identical (5.5 mph west).
- Luigi and Jasmine: Luigi went east and Jasmine went south, with different displacements (4.3 mph east vs. 4.0 mph south).
- Logan and Jasmine: Logan went north and Jasmine went south, with the same magnitude of displacement (4.0 mph north vs. 4.0 mph south) in opposite directions.
Now, let's evaluate each statement:
1. Statement 1: Garreth and Elisa ran the same distance but not the same displacement, Luigi and Jasmine went the same displacement, and Logan ran faster than Jasmine.
- False. Gareth and Elisa ran the same distance and had the same displacement. Luigi and Jasmine did not have the same displacement.
2. Statement 2: Garreth ran farther than Luigi, Elisa and Jasmine went the same distance, and Logan and Jasmine have the same displacement in opposite directions.
- False. Elisa and Jasmine did not go the same distance.
3. Statement 3: Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.
- False. Luigi and Jasmine did not go the same distance.
4. Statement 4: Garreth ran less than Logan, Elisa and Jasmine went the same displacement, and Luigi and Garreth ran together.
- False. Gareth ran more than Logan. Elisa and Jasmine did not go the same displacement.
After evaluating the statements, none of the statements correctly describe the situation. Hence, the answer is:
None of the statements are correct.
1. Distance Ran by Each Runner:
- Gareth:
- Time: 40 minutes (which is [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex] hours)
- Speed: 6.2 mph
- Distance: [tex]\(6.2 \, \text{mph} \times \frac{2}{3} \, \text{hours} = \frac{12.4}{3} \approx 4.13 \, \text{miles}\)[/tex]
- Luigi:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 6.0 mph
- Distance: [tex]\(6.0 \, \text{mph} \times 0.583 \, \text{hours} \approx 3.50 \, \text{miles}\)[/tex]
- Elisa:
- Time: 40 minutes (which is [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex] hours)
- Speed: 6.2 mph
- Distance: [tex]\(6.2 \, \text{mph} \times \frac{2}{3} \, \text{hours} = \frac{12.4}{3} \approx 4.13 \, \text{miles}\)[/tex]
- Jasmine:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 5.0 mph
- Distance: [tex]\(5.0 \, \text{mph} \times 0.583 \, \text{hours} \approx 2.92 \, \text{miles}\)[/tex]
- Logan:
- Time: 35 minutes (which is [tex]\(\frac{35}{60} \approx 0.583\)[/tex] hours)
- Speed: 5.6 mph
- Distance: [tex]\(5.6 \, \text{mph} \times 0.583 \, \text{hours} \approx 3.26 \, \text{miles}\)[/tex]
2. Displacements:
- Garreth and Elisa: Both ran west at speeds resulting in the same distance of approximately 4.13 miles, but their displacement is identical (5.5 mph west).
- Luigi and Jasmine: Luigi went east and Jasmine went south, with different displacements (4.3 mph east vs. 4.0 mph south).
- Logan and Jasmine: Logan went north and Jasmine went south, with the same magnitude of displacement (4.0 mph north vs. 4.0 mph south) in opposite directions.
Now, let's evaluate each statement:
1. Statement 1: Garreth and Elisa ran the same distance but not the same displacement, Luigi and Jasmine went the same displacement, and Logan ran faster than Jasmine.
- False. Gareth and Elisa ran the same distance and had the same displacement. Luigi and Jasmine did not have the same displacement.
2. Statement 2: Garreth ran farther than Luigi, Elisa and Jasmine went the same distance, and Logan and Jasmine have the same displacement in opposite directions.
- False. Elisa and Jasmine did not go the same distance.
3. Statement 3: Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.
- False. Luigi and Jasmine did not go the same distance.
4. Statement 4: Garreth ran less than Logan, Elisa and Jasmine went the same displacement, and Luigi and Garreth ran together.
- False. Gareth ran more than Logan. Elisa and Jasmine did not go the same displacement.
After evaluating the statements, none of the statements correctly describe the situation. Hence, the answer is:
None of the statements are correct.
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