Answer :
Let's analyze the problem step-by-step based on the given data.
1. Convert the times into hours:
- Gareth ran for [tex]\( \frac{40}{60} \)[/tex] hours = 0.6667 hours.
- Lung ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
- Elise ran for [tex]\( \frac{40}{60} \)[/tex] hours = 0.6667 hours.
- Jasmine ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
- Logan ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
2. Calculate the distances each runner covered using the formula [tex]\( \text{distance} = \text{speed} \times \text{time} \)[/tex]:
- Gareth: 6.2 mph 0.6667 hours = 4.13 miles.
- Lung: 5.0 mph 0.5833 hours = 2.92 miles.
- Elise: 6.2 mph 0.6667 hours = 4.13 miles.
- Jasmine: 5.0 mph 0.5833 hours = 2.92 miles.
- Logan: 5.6 mph 0.5833 hours = 3.27 miles.
3. Calculate the displacement for each runner using the formula [tex]\( \text{displacement} = \text{velocity} \times \text{time} \)[/tex]:
- Gareth: 5.5 mph west 0.6667 hours = 3.67 miles west.
- Lung: 4.3 mph east 0.5833 hours = 2.5 miles east.
- Elise: 5.5 mph west 0.6667 hours = 3.67 miles west.
- Jasmine: 4.0 mph south 0.5833 hours = 2.33 miles south.
- Logan: 4.0 mph north 0.5833 hours = 2.33 miles north.
4. Analyze the statements based on the calculated distances and displacements:
- Gareth and Elise ran the same distance (4.13 miles) but did not have the same displacement. Both have a displacement of 3.67 miles, but in the same direction (west), so this part is incorrect.
- Lung and Jasmine did not have the same displacement. Lung has 2.5 miles east, Jasmine has 2.33 miles south, so this part is incorrect.
- Logan ran faster than Jasmine. Logan covered 3.27 miles while Jasmine covered 2.92 miles, so this part is correct.
- Gareth ran farther than Lung. Gareth ran 4.13 miles, and Lung ran 2.92 miles, so this part is correct.
- Elise and Jasmine did not run the same distance. Elise ran 4.13 miles, and Jasmine ran 2.92 miles, so this part is incorrect.
- Logan and Jasmine have the same displacement in opposite directions. Both have a displacement of 2.33 miles, in north and south respectively, so this part is correct.
Given all this information, the statement that best describes the runners is:
"Garreth ran farther than Lung, Elisa and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction."
However, considering the corrections made in distances and displacements compared to the choices provided, we conclude the original Python solution used is correct and the most accurate statement is:
Gareth and Elise ran the same distance but not the same displacement, Logan and Jasmine have the same displacement in the opposite direction, and Logan ran faster than Jasmine. Gareth ran farther than Lung.
1. Convert the times into hours:
- Gareth ran for [tex]\( \frac{40}{60} \)[/tex] hours = 0.6667 hours.
- Lung ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
- Elise ran for [tex]\( \frac{40}{60} \)[/tex] hours = 0.6667 hours.
- Jasmine ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
- Logan ran for [tex]\( \frac{35}{60} \)[/tex] hours = 0.5833 hours.
2. Calculate the distances each runner covered using the formula [tex]\( \text{distance} = \text{speed} \times \text{time} \)[/tex]:
- Gareth: 6.2 mph 0.6667 hours = 4.13 miles.
- Lung: 5.0 mph 0.5833 hours = 2.92 miles.
- Elise: 6.2 mph 0.6667 hours = 4.13 miles.
- Jasmine: 5.0 mph 0.5833 hours = 2.92 miles.
- Logan: 5.6 mph 0.5833 hours = 3.27 miles.
3. Calculate the displacement for each runner using the formula [tex]\( \text{displacement} = \text{velocity} \times \text{time} \)[/tex]:
- Gareth: 5.5 mph west 0.6667 hours = 3.67 miles west.
- Lung: 4.3 mph east 0.5833 hours = 2.5 miles east.
- Elise: 5.5 mph west 0.6667 hours = 3.67 miles west.
- Jasmine: 4.0 mph south 0.5833 hours = 2.33 miles south.
- Logan: 4.0 mph north 0.5833 hours = 2.33 miles north.
4. Analyze the statements based on the calculated distances and displacements:
- Gareth and Elise ran the same distance (4.13 miles) but did not have the same displacement. Both have a displacement of 3.67 miles, but in the same direction (west), so this part is incorrect.
- Lung and Jasmine did not have the same displacement. Lung has 2.5 miles east, Jasmine has 2.33 miles south, so this part is incorrect.
- Logan ran faster than Jasmine. Logan covered 3.27 miles while Jasmine covered 2.92 miles, so this part is correct.
- Gareth ran farther than Lung. Gareth ran 4.13 miles, and Lung ran 2.92 miles, so this part is correct.
- Elise and Jasmine did not run the same distance. Elise ran 4.13 miles, and Jasmine ran 2.92 miles, so this part is incorrect.
- Logan and Jasmine have the same displacement in opposite directions. Both have a displacement of 2.33 miles, in north and south respectively, so this part is correct.
Given all this information, the statement that best describes the runners is:
"Garreth ran farther than Lung, Elisa and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction."
However, considering the corrections made in distances and displacements compared to the choices provided, we conclude the original Python solution used is correct and the most accurate statement is:
Gareth and Elise ran the same distance but not the same displacement, Logan and Jasmine have the same displacement in the opposite direction, and Logan ran faster than Jasmine. Gareth ran farther than Lung.
