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Dynamic Transportation Optimization: Worksheet 2 - Beginner Practice Dynamic Transportation Optimization BEGINNER

Ready to master Dynamic Transportation Optimization? This entry level practice worksheet (2/10) presents 20 beginner-level challenges. Focus area: pattern recognition. Learn to solve dynamic transportation optimization reasoning questions, handle dynamic transportation optimization practice, and perfect dynamic transportation optimization for competitive exams with our step-by-step solutions.

📝 Worksheet 2 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

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Worksheet 2 of 10 (11% complete)

Question 1

A passenger travels from Denver to Dallas via Atlanta. The minimum layover at Atlanta is **60 minutes**. **Flights Denver -> Atlanta:** - F1-1: Dep 7:30 AM, Arr 9:32 AM - F1-2: Dep 10:30 AM, Arr 12:32 PM - F1-3: Dep 1:30 PM, Arr 3:32 PM **Flights Atlanta -> Dallas:** - F2-1: Dep 11:30 AM, Arr 3:23 PM - F2-2: Dep 1:30 PM, Arr 5:23 PM - F2-3: Dep 3:30 PM, Arr 7:23 PM What is the minimum total elapsed time for the journey from Denver to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 473 minutes is achieved by combining F1-1 (Arr: 9:32 AM) and F2-1 (Dep: 11:30 AM, Arr: 3:23 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 53 minutes.

Question 2

A passenger travels from Denver to Chicago via Miami. The minimum layover at Miami is **90 minutes**. **Flights Denver -> Miami:** - F1-1: Dep 8:00 AM, Arr 10:44 AM - F1-2: Dep 11:00 AM, Arr 1:44 PM - F1-3: Dep 2:00 PM, Arr 4:44 PM **Flights Miami -> Chicago:** - F2-1: Dep 12:00 PM, Arr 3:10 PM - F2-2: Dep 2:00 PM, Arr 5:10 PM - F2-3: Dep 4:00 PM, Arr 7:10 PM What is the minimum total elapsed time for the journey from Denver to Chicago?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 490 minutes is achieved by combining F1-2 (Arr: 1:44 PM) and F2-3 (Dep: 4:00 PM, Arr: 7:10 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 8 hours and 10 minutes.

Question 3

A passenger travels from Chicago to Miami via Denver. The minimum layover at Denver is **60 minutes**. **Flights Chicago -> Denver:** - F1-1: Dep 5:30 AM, Arr 8:13 AM - F1-2: Dep 8:30 AM, Arr 11:13 AM - F1-3: Dep 11:30 AM, Arr 2:13 PM **Flights Denver -> Miami:** - F2-1: Dep 10:30 AM, Arr 1:28 PM - F2-2: Dep 12:30 PM, Arr 3:28 PM - F2-3: Dep 2:30 PM, Arr 5:28 PM What is the minimum total elapsed time for the journey from Chicago to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 418 minutes is achieved by combining F1-2 (Arr: 11:13 AM) and F2-2 (Dep: 12:30 PM, Arr: 3:28 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 58 minutes.

Question 4

A passenger travels from Denver to Atlanta via Dallas. The minimum layover at Dallas is **90 minutes**. **Flights Denver -> Dallas:** - F1-1: Dep 7:30 AM, Arr 9:41 AM - F1-2: Dep 10:30 AM, Arr 12:41 PM - F1-3: Dep 1:30 PM, Arr 3:41 PM **Flights Dallas -> Atlanta:** - F2-1: Dep 12:00 PM, Arr 2:41 PM - F2-2: Dep 2:00 PM, Arr 4:41 PM - F2-3: Dep 4:00 PM, Arr 6:41 PM What is the minimum total elapsed time for the journey from Denver to Atlanta?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 431 minutes is achieved by combining F1-1 (Arr: 9:41 AM) and F2-1 (Dep: 12:00 PM, Arr: 2:41 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 11 minutes.

Question 5

A passenger travels from Chicago to Miami via Dallas. The minimum layover at Dallas is **60 minutes**. **Flights Chicago -> Dallas:** - F1-1: Dep 8:30 AM, Arr 11:10 AM - F1-2: Dep 11:30 AM, Arr 2:10 PM - F1-3: Dep 2:30 PM, Arr 5:10 PM **Flights Dallas -> Miami:** - F2-1: Dep 1:00 PM, Arr 4:10 PM - F2-2: Dep 3:00 PM, Arr 6:10 PM - F2-3: Dep 5:00 PM, Arr 8:10 PM What is the minimum total elapsed time for the journey from Chicago to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 460 minutes is achieved by combining F1-1 (Arr: 11:10 AM) and F2-1 (Dep: 1:00 PM, Arr: 4:10 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 40 minutes.

Question 6

A passenger travels from Atlanta to Denver via Dallas. The minimum layover at Dallas is **90 minutes**. **Flights Atlanta -> Dallas:** - F1-1: Dep 7:30 AM, Arr 9:08 AM - F1-2: Dep 10:30 AM, Arr 12:08 PM - F1-3: Dep 1:30 PM, Arr 3:08 PM **Flights Dallas -> Denver:** - F2-1: Dep 1:30 PM, Arr 3:41 PM - F2-2: Dep 3:30 PM, Arr 5:41 PM - F2-3: Dep 5:30 PM, Arr 7:41 PM What is the minimum total elapsed time for the journey from Atlanta to Denver?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 371 minutes is achieved by combining F1-3 (Arr: 3:08 PM) and F2-3 (Dep: 5:30 PM, Arr: 7:41 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 11 minutes.

Question 7

A passenger travels from Miami to Dallas via Chicago. The minimum layover at Chicago is **90 minutes**. **Flights Miami -> Chicago:** - F1-1: Dep 6:30 AM, Arr 9:09 AM - F1-2: Dep 9:30 AM, Arr 12:09 PM - F1-3: Dep 12:30 PM, Arr 3:09 PM **Flights Chicago -> Dallas:** - F2-1: Dep 12:30 PM, Arr 4:15 PM - F2-2: Dep 2:30 PM, Arr 6:15 PM - F2-3: Dep 4:30 PM, Arr 8:15 PM What is the minimum total elapsed time for the journey from Miami to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 525 minutes is achieved by combining F1-2 (Arr: 12:09 PM) and F2-2 (Dep: 2:30 PM, Arr: 6:15 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 8 hours and 45 minutes.

Question 8

A passenger travels from Denver to Dallas via Chicago. The minimum layover at Chicago is **90 minutes**. **Flights Denver -> Chicago:** - F1-1: Dep 7:00 AM, Arr 9:18 AM - F1-2: Dep 10:00 AM, Arr 12:18 PM - F1-3: Dep 1:00 PM, Arr 3:18 PM **Flights Chicago -> Dallas:** - F2-1: Dep 2:30 PM, Arr 5:32 PM - F2-2: Dep 4:30 PM, Arr 7:32 PM - F2-3: Dep 6:30 PM, Arr 9:32 PM What is the minimum total elapsed time for the journey from Denver to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 452 minutes is achieved by combining F1-2 (Arr: 12:18 PM) and F2-1 (Dep: 2:30 PM, Arr: 5:32 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 32 minutes.

Question 9

A passenger travels from Miami to Dallas via Atlanta. The minimum layover at Atlanta is **45 minutes**. **Flights Miami -> Atlanta:** - F1-1: Dep 7:00 AM, Arr 9:41 AM - F1-2: Dep 10:00 AM, Arr 12:41 PM - F1-3: Dep 1:00 PM, Arr 3:41 PM **Flights Atlanta -> Dallas:** - F2-1: Dep 11:30 AM, Arr 2:58 PM - F2-2: Dep 1:30 PM, Arr 4:58 PM - F2-3: Dep 3:30 PM, Arr 6:58 PM What is the minimum total elapsed time for the journey from Miami to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 418 minutes is achieved by combining F1-2 (Arr: 12:41 PM) and F2-2 (Dep: 1:30 PM, Arr: 4:58 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 58 minutes.

Question 10

A passenger travels from Miami to Chicago via Denver. The minimum layover at Denver is **60 minutes**. **Flights Miami -> Denver:** - F1-1: Dep 6:30 AM, Arr 8:14 AM - F1-2: Dep 9:30 AM, Arr 11:14 AM - F1-3: Dep 12:30 PM, Arr 2:14 PM **Flights Denver -> Chicago:** - F2-1: Dep 10:30 AM, Arr 2:14 PM - F2-2: Dep 12:30 PM, Arr 4:14 PM - F2-3: Dep 2:30 PM, Arr 6:14 PM What is the minimum total elapsed time for the journey from Miami to Chicago?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 404 minutes is achieved by combining F1-2 (Arr: 11:14 AM) and F2-2 (Dep: 12:30 PM, Arr: 4:14 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 44 minutes.

Question 11

A passenger travels from Denver to Dallas via Miami. The minimum layover at Miami is **45 minutes**. **Flights Denver -> Miami:** - F1-1: Dep 5:30 AM, Arr 7:36 AM - F1-2: Dep 8:30 AM, Arr 10:36 AM - F1-3: Dep 11:30 AM, Arr 1:36 PM **Flights Miami -> Dallas:** - F2-1: Dep 12:30 PM, Arr 2:52 PM - F2-2: Dep 2:30 PM, Arr 4:52 PM - F2-3: Dep 4:30 PM, Arr 6:52 PM What is the minimum total elapsed time for the journey from Denver to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 322 minutes is achieved by combining F1-3 (Arr: 1:36 PM) and F2-2 (Dep: 2:30 PM, Arr: 4:52 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 5 hours and 22 minutes.

Question 12

A passenger travels from Denver to Atlanta via Chicago. The minimum layover at Chicago is **45 minutes**. **Flights Denver -> Chicago:** - F1-1: Dep 7:00 AM, Arr 9:45 AM - F1-2: Dep 10:00 AM, Arr 12:45 PM - F1-3: Dep 1:00 PM, Arr 3:45 PM **Flights Chicago -> Atlanta:** - F2-1: Dep 1:30 PM, Arr 4:07 PM - F2-2: Dep 3:30 PM, Arr 6:07 PM - F2-3: Dep 5:30 PM, Arr 8:07 PM What is the minimum total elapsed time for the journey from Denver to Atlanta?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 367 minutes is achieved by combining F1-2 (Arr: 12:45 PM) and F2-1 (Dep: 1:30 PM, Arr: 4:07 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 7 minutes.

Question 13

A passenger travels from Miami to Atlanta via Denver. The minimum layover at Denver is **90 minutes**. **Flights Miami -> Denver:** - F1-1: Dep 8:30 AM, Arr 11:08 AM - F1-2: Dep 11:30 AM, Arr 2:08 PM - F1-3: Dep 2:30 PM, Arr 5:08 PM **Flights Denver -> Atlanta:** - F2-1: Dep 2:00 PM, Arr 4:44 PM - F2-2: Dep 4:00 PM, Arr 6:44 PM - F2-3: Dep 6:00 PM, Arr 8:44 PM What is the minimum total elapsed time for the journey from Miami to Atlanta?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 434 minutes is achieved by combining F1-2 (Arr: 2:08 PM) and F2-2 (Dep: 4:00 PM, Arr: 6:44 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 14 minutes.

Question 14

A passenger travels from Atlanta to Miami via Chicago. The minimum layover at Chicago is **45 minutes**. **Flights Atlanta -> Chicago:** - F1-1: Dep 6:00 AM, Arr 8:07 AM - F1-2: Dep 9:00 AM, Arr 11:07 AM - F1-3: Dep 12:00 PM, Arr 2:07 PM **Flights Chicago -> Miami:** - F2-1: Dep 12:00 PM, Arr 2:32 PM - F2-2: Dep 2:00 PM, Arr 4:32 PM - F2-3: Dep 4:00 PM, Arr 6:32 PM What is the minimum total elapsed time for the journey from Atlanta to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 332 minutes is achieved by combining F1-2 (Arr: 11:07 AM) and F2-1 (Dep: 12:00 PM, Arr: 2:32 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 5 hours and 32 minutes.

Question 15

A passenger travels from Chicago to Dallas via Miami. The minimum layover at Miami is **45 minutes**. **Flights Chicago -> Miami:** - F1-1: Dep 6:30 AM, Arr 8:59 AM - F1-2: Dep 9:30 AM, Arr 11:59 AM - F1-3: Dep 12:30 PM, Arr 2:59 PM **Flights Miami -> Dallas:** - F2-1: Dep 2:30 PM, Arr 5:48 PM - F2-2: Dep 4:30 PM, Arr 7:48 PM - F2-3: Dep 6:30 PM, Arr 9:48 PM What is the minimum total elapsed time for the journey from Chicago to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 438 minutes is achieved by combining F1-3 (Arr: 2:59 PM) and F2-2 (Dep: 4:30 PM, Arr: 7:48 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 18 minutes.

Question 16

A passenger travels from Chicago to Miami via Atlanta. The minimum layover at Atlanta is **60 minutes**. **Flights Chicago -> Atlanta:** - F1-1: Dep 8:00 AM, Arr 10:38 AM - F1-2: Dep 11:00 AM, Arr 1:38 PM - F1-3: Dep 2:00 PM, Arr 4:38 PM **Flights Atlanta -> Miami:** - F2-1: Dep 2:00 PM, Arr 4:49 PM - F2-2: Dep 4:00 PM, Arr 6:49 PM - F2-3: Dep 6:00 PM, Arr 8:49 PM What is the minimum total elapsed time for the journey from Chicago to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 409 minutes is achieved by combining F1-3 (Arr: 4:38 PM) and F2-3 (Dep: 6:00 PM, Arr: 8:49 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 49 minutes.

Question 17

A passenger travels from Atlanta to Miami via Chicago. The minimum layover at Chicago is **90 minutes**. **Flights Atlanta -> Chicago:** - F1-1: Dep 9:00 AM, Arr 11:38 AM - F1-2: Dep 12:00 PM, Arr 2:38 PM - F1-3: Dep 3:00 PM, Arr 5:38 PM **Flights Chicago -> Miami:** - F2-1: Dep 11:00 AM, Arr 1:16 PM - F2-2: Dep 1:00 PM, Arr 3:16 PM - F2-3: Dep 3:00 PM, Arr 5:16 PM What is the minimum total elapsed time for the journey from Atlanta to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 496 minutes is achieved by combining F1-1 (Arr: 11:38 AM) and F2-3 (Dep: 3:00 PM, Arr: 5:16 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 8 hours and 16 minutes.

Question 18

A passenger travels from Dallas to Atlanta via Miami. The minimum layover at Miami is **60 minutes**. **Flights Dallas -> Miami:** - F1-1: Dep 8:00 AM, Arr 10:43 AM - F1-2: Dep 11:00 AM, Arr 1:43 PM - F1-3: Dep 2:00 PM, Arr 4:43 PM **Flights Miami -> Atlanta:** - F2-1: Dep 10:00 AM, Arr 12:44 PM - F2-2: Dep 12:00 PM, Arr 2:44 PM - F2-3: Dep 2:00 PM, Arr 4:44 PM What is the minimum total elapsed time for the journey from Dallas to Atlanta?
1. Timeline Approach & Constraint Application (Minimum Layover: 60 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 404 minutes is achieved by combining F1-1 (Arr: 10:43 AM) and F2-2 (Dep: 12:00 PM, Arr: 2:44 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 44 minutes.

Question 19

A passenger travels from Denver to Atlanta via Chicago. The minimum layover at Chicago is **45 minutes**. **Flights Denver -> Chicago:** - F1-1: Dep 7:00 AM, Arr 9:50 AM - F1-2: Dep 10:00 AM, Arr 12:50 PM - F1-3: Dep 1:00 PM, Arr 3:50 PM **Flights Chicago -> Atlanta:** - F2-1: Dep 1:00 PM, Arr 3:53 PM - F2-2: Dep 3:00 PM, Arr 5:53 PM - F2-3: Dep 5:00 PM, Arr 7:53 PM What is the minimum total elapsed time for the journey from Denver to Atlanta?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 413 minutes is achieved by combining F1-3 (Arr: 3:50 PM) and F2-3 (Dep: 5:00 PM, Arr: 7:53 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 6 hours and 53 minutes.

Question 20

A passenger travels from Denver to Miami via Atlanta. The minimum layover at Atlanta is **45 minutes**. **Flights Denver -> Atlanta:** - F1-1: Dep 6:30 AM, Arr 9:21 AM - F1-2: Dep 9:30 AM, Arr 12:21 PM - F1-3: Dep 12:30 PM, Arr 3:21 PM **Flights Atlanta -> Miami:** - F2-1: Dep 12:00 PM, Arr 3:10 PM - F2-2: Dep 2:00 PM, Arr 5:10 PM - F2-3: Dep 4:00 PM, Arr 7:10 PM What is the minimum total elapsed time for the journey from Denver to Miami?
1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 460 minutes is achieved by combining F1-2 (Arr: 12:21 PM) and F2-2 (Dep: 2:00 PM, Arr: 5:10 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 40 minutes.
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