To determine the minimum number of trains required for the service between two stations that are 60 km apart, we need to analyze the movement of the trains and their schedules. Let’s break this down step by step.
Understanding the Train Journey
Each train travels at a constant speed of 60 km/h. Given that the distance between the two stations is 60 km, we can calculate the time it takes for a train to travel from one station to the other.
Calculating Travel Time
The time taken for a train to travel 60 km at 60 km/h is:
- Time = Distance / Speed
- Time = 60 km / 60 km/h = 1 hour
So, each train takes 1 hour to reach the opposite station.
Considering the Halt Time
Once a train reaches either station, it halts for 20 minutes before turning back. This halt time needs to be factored into our calculations.
Calculating Total Round Trip Time
The total time for a round trip (to the opposite station and back) can be calculated as follows:
- Time to reach the opposite station: 1 hour
- Halt time at the station: 20 minutes (which is 1/3 hour)
- Time to return to the starting station: 1 hour
Thus, the total round trip time is:
- Total time = 1 hour + 1/3 hour + 1 hour = 2 hours and 20 minutes
Train Departure Frequency
Trains depart every 10 minutes from each station. This means that in one hour, there will be:
- 6 departures from each station (since 60 minutes / 10 minutes = 6).
Calculating the Number of Trains Needed
Now, let’s analyze how many trains are needed to maintain this schedule. Since each train takes 2 hours and 20 minutes for a round trip, we need to ensure that there are enough trains to cover the departures during this time.
- Convert 2 hours and 20 minutes into minutes: 2 hours = 120 minutes + 20 minutes = 140 minutes.
- In 140 minutes, how many trains can depart every 10 minutes? This is calculated as:
- 140 minutes / 10 minutes = 14 departures.
However, since we need to account for the fact that trains are still in transit during their round trip, we need to add one more train to ensure that there is always a train available for the next departure. Therefore, the total number of trains required is:
- 14 (for the round trip) + 2 (one for each station to ensure continuous service) = 16 trains.
Final Thoughts
In summary, to maintain a consistent service with trains departing every 10 minutes and accounting for travel and halt times, a total of 16 trains is required. This ensures that there are always trains available for departure while others are en route or halted at the stations.
