A train is scheduled to cover the distance between two stations 46 km apart in one hour. If it travels 25 km at a speed of 40 km/hr, find the speed for the remaining journey to complete it in the scheduled time.

### Concept & Formula Find the time remaining by subtracting the time already spent from the total scheduled time, then calculate the required speed for the remaining distance. $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$ ### Step-by-Step Solution * **Given:** * Total distance = $46$ km * Scheduled total time = $1$ hour * **First Part of Journey:** * Distance = $25$ km * Speed = $40$ km/hr * Time taken = $\frac{25}{40} = \frac{5}{8}$ hours * **Remaining Journey:** * Remaining distance = $46 - 25 = 21$ km * Remaining time = $1 - \frac{5}{8} = \frac{3}{8}$ hours * **Required Speed:** * Speed = $\frac{\text{Distance}}{\text{Time}} = \frac{21}{3/8} = 21 \times \frac{8}{3}$ * Speed = $7 \times 8 = 56$ km/hr ### Exam Strategy & Shortcut Using fractions ($\frac{5}{8}$ and $\frac{3}{8}$) instead of decimals ($0.625$ and $0.375$) makes the final multiplication much faster and less prone to arithmetic mistakes. ### Common Pitfall Using decimals for $\frac{25}{40}$ can make the subsequent division $\frac{21}{0.375}$ overly complicated to calculate manually under time pressure. ### Final Answer Therefore, the correct answer is **56 km/hr**.