Question 1
A passenger travels from Dallas to Miami via Chicago. The minimum layover at Chicago is **90 minutes**.
**Flights Dallas -> Chicago:**
- F1-1: Dep 6:00 AM, Arr 8:56 AM
- F1-2: Dep 9:00 AM, Arr 11:56 AM
- F1-3: Dep 12:00 PM, Arr 2:56 PM
**Flights Chicago -> Miami:**
- F2-1: Dep 1:30 PM, Arr 4:18 PM
- F2-2: Dep 3:30 PM, Arr 6:18 PM
- F2-3: Dep 5:30 PM, Arr 8:18 PM
What is the minimum total elapsed time for the journey from Dallas 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 438 minutes is achieved by combining F1-2 (Arr: 11:56 AM) and F2-1 (Dep: 1:30 PM, Arr: 4:18 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.
3. Final Answer: The minimum elapsed time is 7 hours and 18 minutes.
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 F1-2 (Arr: 11:56 AM) and F2-1 (Dep: 1:30 PM, Arr: 4:18 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.
3. Final Answer: The minimum elapsed time is 7 hours and 18 minutes.