Answered

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 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
Let's look at what the data tells us about each runner and verify our conditions step-by-step.

### Summary of Given Data

1. Garreth:
- Time: 40 minutes
- Speed: 6.2 mph
- Velocity: 5.5 mph west

2. Luigi:
- Time: 35 minutes
- Speed: 5.0 mph
- Velocity: 4.3 mph east

3. Elisa:
- Time: 40 minutes
- Speed: 6.2 mph
- Velocity: 5.5 mph west

4. Jasmine:
- Time: 35 minutes
- Speed: 5.0 mph
- Velocity: 4.0 mph south

5. Logan:
- Time: 35 minutes
- Speed: 5.6 mph
- Velocity: 4.0 mph north

### Calculating Distance Covered by Each Runner

Distance = Time Speed

1. Garreth:
- Time: 40 minutes = 40/60 hours = 2/3 hours
- Speed: 6.2 mph
- Distance: (2/3) 6.2 = 4.13 miles

2. Luigi:
- Time: 35 minutes = 35/60 hours = 7/12 hours
- Speed: 5.0 mph
- Distance: (7/12) 5.0 = 2.92 miles

3. Elisa:
- Time: 40 minutes = 40/60 hours = 2/3 hours
- Speed: 6.2 mph
- Distance: (2/3) 6.2 = 4.13 miles

4. Jasmine:
- Time: 35 minutes = 35/60 hours = 7/12 hours
- Speed: 5.0 mph
- Distance: (7/12) 5.0 = 2.92 miles

5. Logan:
- Time: 35 minutes = 35/60 hours = 7/12 hours
- Speed: 5.6 mph
- Distance: (7/12) 5.6 = 3.27 miles

### Checking Each Condition

#### Option 1:
1. Garreth and Elisa ran the same distance but not the same displacement.
- Distance: Garreth = 4.13 miles, Elisa = 4.13 miles (same)
- Displacement: Garreth = 5.5 mph west, Elisa = 5.5 mph west (same direction, thus same displacement)

This condition is not satisfied because Garreth and Elisa ran the same distance and direction, resulting in the same displacement.

#### Option 2:
1. Garreth ran farther than Luigi.
- Garreth: 4.13 miles
- Luigi: 2.92 miles
Clearly, this condition is true since 4.13 > 2.92.

2. Elisa and Jasmine went the same distance.
- Elisa: 4.13 miles
- Jasmine: 2.92 miles
This condition is not satisfied because their distances are different.

3. Logan and Jasmine have the same displacement in the opposite direction.
- Logan: 4.0 mph north
- Jasmine: 4.0 mph south
This condition is true.

Since the second condition is not satisfied, this option is not fully correct.

#### Option 3:
1. Garreth and Elisa ran together.
- Distances: Both ran 4.13 miles
- Directions: Both in the same direction (west)
This condition is satisfied.

2. Luigi and Jasmine went the same distance.
- Luigi: 2.92 miles
- Jasmine: 2.92 miles
This condition is satisfied.

3. Logan and Jasmine have the same displacement in the opposite direction.
- Velocity: Logan = 4.0 mph north, Jasmine = 4.0 mph south
This condition is satisfied.

All the conditions for option 3 are satisfied.

#### Option 4:
1. Garreth ran less than Logan.
- Garreth: 4.13 miles
- Logan: 3.27 miles
This condition is not satisfied because 4.13 > 3.27.

Since the first condition is not satisfied, this option is not correct.

### Conclusion
After verifying the provided data and checking each option, Option 3 is the best fit:

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

Thus, the answer is:
[tex]\[ \boxed{3} \][/tex]

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