IDNLearn.com offers a comprehensive solution for finding accurate answers quickly. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.
Sagot :
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]
### 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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.
