Train travel time between stations A and B is 39 hours. Every day a pair of trains leave from A to B and B to A at 6 AM. If the service starts on a Monday, on which earliest day will the same train rakes start the journeys again from their original stations?
Friday
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.
Important Questions from Problem on Trains
- A train with a length of 195 m overtakes a man moving at a speed of 5 km/hr (in the same direction) in 13 seconds. How much time (in seconds) will it take this train to completely cross another train that is 255 m long, moving in the opposite direction at a speed of 76 km/hr?
- Train A leaves station M at 8:25 AM and reaches station N at 3:25 PM on the same day. Train B leaves station N at 10:25 AM and reaches station M at 3:25 PM on the same day. Find the time when trains A and B meet.
- A train of length 490 m overtakes a man moving at a speed of 9 km/hr (in the same direction) in 12 seconds. How much time (in seconds) will it take this train to completely cross another train that has is 500 m long, moving in the opposite direction at a speed of 42 km/hr?
- Train A leaves station M at 7:55 a.m. and reaches station N at 2:55 p.m. on the same day. Train B leaves station N at 9:55 a.m. and reaches station M at 2:55 p.m. on the same day. Find the time when Trains A and B meet.
Train A leaves station M at 6:40 AM and reaches station N at 3:40 PM on the same day. Train B leaves station N at 8:40 AM and reaches station M at 2:40 PM on the same day. Find the time when trains A and B meet.
