Question 1
A passenger travels from Dallas to Atlanta via Miami. The minimum layover at Miami is **45 minutes**.
**Flights Dallas -> Miami:**
- F1-1: Dep 5:00 AM, Arr 7:13 AM
- F1-2: Dep 8:00 AM, Arr 10:13 AM
- F1-3: Dep 11:00 AM, Arr 1:13 PM
**Flights Miami -> Atlanta:**
- F2-1: Dep 2:30 PM, Arr 6:18 PM
- F2-2: Dep 4:30 PM, Arr 8:18 PM
- F2-3: Dep 6:30 PM, Arr 10:18 PM
What is the minimum total elapsed time for the journey from Dallas 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 438 minutes is achieved by combining F1-3 (Arr: 1:13 PM) and F2-1 (Dep: 2:30 PM, Arr: 6:18 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 F1-3 (Arr: 1:13 PM) and F2-1 (Dep: 2:30 PM, Arr: 6:18 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.
3. Final Answer: The minimum elapsed time is 7 hours and 18 minutes.