Final answer:
The average speed of the train for the entire journey, given that it travels equal distances at 60 km/hr and 40 km/hr, is 48 km/hr.
Step-by-step explanation:
The student has asked about calculating the average speed of a train that travels two equal distances at different speeds. To calculate the average speed, we need to know the total distance traveled and the total time taken for the entire journey.
Let's assume the train travels a certain distance 'd' at 60 km/hr and then the same distance 'd' back at 40 km/hr. The total distance is therefore 2d. The time to travel the first distance 'd' at 60 km/hr is 'd/60' hours, and the time to travel back the same distance 'd' at 40 km/hr is 'd/40' hours.
To find the average speed (Vavg), we use the formula:
Vavg = Total Distance / Total Time
Here, Total Time = (d/60) + (d/40)
We find a common denominator, which is 120 (the LCM of 60 and 40), and get:
Total Time = (2d/120) + (3d/120) = 5d/120
Vavg = 2d / (5d/120) = 2d × (120/5d) = 240d/5d
After canceling 'd', we get:
Vavg = 48 km/hr