Question

the chart indicates the time, speed, and velocity of five runners. which best describes the runners? chart with columns: runner, total time, speed, velocity. rows: gareth (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). options: 1. gareth and elisa ran the same distance but not the same displacement, luigi and jasmine went the same displacement, and logan ran faster than jasmine. 2. gareth ran farther than luigi, elisa and jasmine went the same distance, and logan and jasmine has the same displacement in the opposite direction. 3. gareth and elisa ran together, luigi and jasmine went the same distance, and logan and jasmine have the same displacement in the opposite direction. 4. gareth ran less than logan, elisa and jasmine went the same displacement, and luigi and gareth ran together.

Explanation:

Step1: Calculate distance for each runner

Distance = speed × time (convert time to hours: $\frac{\text{minutes}}{60}$)

• Garreth: $6.2 \times \frac{40}{60} \approx 4.13$ miles
• Luigi: $5.0 \times \frac{35}{60} \approx 2.92$ miles
• Elisa: $6.2 \times \frac{40}{60} \approx 4.13$ miles
• Jasmine: $5.0 \times \frac{35}{60} \approx 2.92$ miles
• Logan: $5.6 \times \frac{35}{60} \approx 3.27$ miles

Step2: Analyze displacement

Displacement = velocity × time (includes direction)

• Garreth/Elisa: Same speed, time, velocity (direction + magnitude) → identical displacement/distance
• Luigi: $4.3 \times \frac{35}{60} \approx 2.51$ miles east
• Jasmine: $4.0 \times \frac{35}{60} \approx 2.33$ miles south
• Logan: $4.0 \times \frac{35}{60} \approx 2.33$ miles north (same magnitude as Jasmine, opposite direction)

Step3: Evaluate each option

Test claims against calculations:

1. 1st option: False (Logan is slower than Garreth/Elisa, Luigi/Jasmine displacement differs)
2. 2nd option: False (Elisa's distance = Garreth's, not Jasmine's)
3. 3rd option: True (Garreth/Elisa match in all metrics; Luigi/Jasmine same distance; Logan/Jasmine same displacement magnitude, opposite direction)
4. 4th option: False (Garreth ran farther than Logan; Elisa/Jasmine displacement differs)

Answer:

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