A train covers the first half of its total journey distance at a speed of 40 km/h . To achieve an overall average speed of 48 km/h for the entire journey, what must be its speed for the second half of the distance?

Step-by-step solution

Let the total distance be 2d . The train covers distance d at v₁ = 40 km/h and the remaining distance d at speed v₂ . For two equal distances covered at different speeds, the average speed v_ avg is given by the harmonic mean: v_ avg = 2 v₁ v₂ v₁ + v₂ Substitute the given values ( v_ avg = 48 km/h and v₁ = 40 km/h ): 48 = 2 40 v₂ 40 + v₂ 48(40 + v₂) = 80 v₂ 1920 + 48 v₂ = 80 v₂ 32 v₂ = 1920 v₂ = 1920 32 = 60 km/h Answer: 60 km/h