1. **State the problem:** We need to find which train takes longer to reach its destination. 2. **Calculate the travel time for the first train:** - Departure: 22:30 - Arrival: 06:40 (next day) Since the arrival is on the next day, calculate the time from 22:30 to midnight (24:00), then add the time from midnight to 06:40. Time from 22:30 to 24:00 is $$24:00 - 22:30 = 1\text{ hour }30\text{ minutes} = 1.5\text{ hours}$$ Time from 00:00 to 06:40 is $$6\text{ hours }40\text{ minutes} = 6 + \frac{40}{60} = 6.6667\text{ hours}$$ Total time for first train is $$1.5 + 6.6667 = 8.1667\text{ hours}$$ 3. **Calculate the travel time for the second train:** - Departure: 20:45 - Arrival: 05:00 (next day) Time from 20:45 to 24:00 is $$24:00 - 20:45 = 3\text{ hours }15\text{ minutes} = 3.25\text{ hours}$$ Time from 00:00 to 05:00 is $$5\text{ hours}$$ Total time for second train is $$3.25 + 5 = 8.25\text{ hours}$$ 4. **Compare the two times:** - First train: 8.1667 hours - Second train: 8.25 hours Since $$8.25 > 8.1667$$, the second train takes longer. **Final answer:** The second train takes longer to reach its destination.