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

\begin{tabular}{|l|l|l|l|}
\hline
Runner & Total time & Speed & Velocity \\
\hline
Garreth & 40 minutes & 6.2 mph & 5.5 mph west \\
\hline
Luigi & 35 minutes & 5.0 mph & 4.3 mph east \\
\hline
Elisa & 40 minutes & 6.2 mph & 5.5 mph west \\
\hline
Jasmine & 35 minutes & 5.0 mph & 4.0 mph south \\
\hline
Logan & 35 minutes & 5.6 mph & 4.0 mph north \\
\hline
\end{tabular}

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 have 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 :

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.