To solve this problem, we can use the concept of average speed. Average speed is calculated as the total distance traveled divided by the total time taken.
Let's denote the speed of the train on the way back (from point Y to point X) as V1 (in km/h). We know the following information:
Distance from X to Y = 300 km Speed from X to Y = 100 km/h Average speed for the entire trip = 120 km/h
To find the speed from Y to X, we need to determine the distance traveled on the way back and the time taken for the return trip.
Distance from Y to X = Distance from X to Y = 300 km
Let's calculate the time taken for the trip from X to Y:
Time taken from X to Y = Distance / Speed = 300 km / 100 km/h = 3 hours
Now, let's calculate the total time taken for the entire trip using the average speed:
Total time = Total distance / Average speed Total time = (300 km + 300 km) / 120 km/h Total time = 600 km / 120 km/h Total time = 5 hours
Since the time taken for the return trip is the difference between the total time and the time taken for the trip from X to Y:
Time taken from Y to X = Total time - Time taken from X to Y Time taken from Y to X = 5 hours - 3 hours Time taken from Y to X = 2 hours
Now, we can calculate the speed from Y to X using the distance and time:
Speed from Y to X = Distance / Time = 300 km / 2 hours = 150 km/h
Therefore, the train traveled from Y to X at a speed of 150 km/h.