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
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
