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The chart indicates the time, speed, and velocity of five runners.

| Runner | Total time | Speed | Velocity |
|--------|------------|---------|-----------------|
| Garreth| 40 minutes | 6.2 mph | 5.5 mph west |
| Luigi | 35 minutes | 5.0 mph | 4.3 mph east |
| Elisa | 40 minutes | 6.2 mph | 5.5 mph west |
| Jasmine| 35 minutes | 5.0 mph | 4.0 mph south |
| Logan | 35 minutes | 5.6 mph | 4.0 mph north |

Which best describes the runners?

A. 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.

B. Garreth ran farther than Luigi, Elisa and Jasmine went the same distance, and Logan and Jasmine had the same displacement in the opposite direction.

C. Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.

D. Garreth ran less than Logan, Elisa and Jasmine went the same displacement, and Luigi and Garreth ran together.



Answer :

GinnyAnswer
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.

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