Train Travel Time Analysis

This problem involves calculating the round trip time for a train rake and determining the earliest day it can start its journey again from its original station, considering a fixed daily departure time.

Let's track the journey of a train rake that starts from station A towards station B.

The train leaves station A on Monday at 6 AM. The travel time from A to B is given as 39 hours.

To find the arrival time at station B, we add 39 hours to the departure time (Monday 6 AM):

• From Monday 6 AM to Tuesday 6 AM is 24 hours.
• Remaining travel time is $39 - 24 = 15$ hours.
• Adding 15 hours to Tuesday 6 AM gives Tuesday 9 PM.

So, the train rake arrives at station B on Tuesday at 9 PM.

This train rake is now at station B. To start its return journey to station A, it must depart from B. Trains depart from B to A every day at 6 AM.

Since the train arrived at B on Tuesday at 9 PM, it cannot depart on Tuesday at 6 AM (as it arrived too late). The earliest it can depart from station B is the next scheduled departure, which is Wednesday at 6 AM.

The return journey from B to A also takes 39 hours. Let's calculate the arrival time back at station A:

• Departure from B: Wednesday 6 AM.
• From Wednesday 6 AM to Thursday 6 AM is 24 hours.
• Remaining travel time is $39 - 24 = 15$ hours.
• Adding 15 hours to Thursday 6 AM gives Thursday 9 PM.

So, the train rake arrives back at station A on Thursday at 9 PM.

This train rake is now back at its original station A. To start its journey to B again, it must depart from A. Trains depart from A to B every day at 6 AM.

Since the train arrived back at A on Thursday at 9 PM, it cannot depart on Thursday at 6 AM (as it arrived too late). The earliest it can depart from station A is the next scheduled departure, which is Friday at 6 AM.

The same logic applies to the train rake that starts from station B towards station A on Monday 6 AM. It will arrive at A on Tuesday 9 PM, depart back to B on Wednesday 6 AM, arrive back at B on Thursday 9 PM, and be ready to depart for A again on Friday 6 AM.

Both train rakes complete their round trips and are back at their original stations by Thursday 9 PM. The earliest they can start their next journey from their original stations is the next scheduled departure time, which is Friday 6 AM.

Therefore, the earliest day the same train rakes will start their journeys again from their original stations is Friday.