A train travels the first one-third of the total distance between two stations at a constant speed of 30 km/h . It covers the remaining two-thirds of the distance at a constant speed of 90 km/h . The average speed of the train for the entire journey is:

Step-by-step solution

Let the total distance be d . Time taken to cover the first one-third of the distance is t₁ = d/3 30 = d 90 . Time taken to cover the remaining two-thirds of the distance is t₂ = 2d/3 90 = 2d 270 = d 135 . Total time taken for the entire journey is t = t₁ + t₂ = d 90 + d 135 = 3d + 2d 270 = 5d 270 = d 54 . Average speed is given by the total distance divided by the total time: v_ avg = d t = d d/54 = 54 km/h . Answer: 54 km/h