An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point? (M.A.T., 2003)

### Concept & Logic Total travel time includes the active driving time plus the accumulated stationary time from all intermediate stops. The final destination does not count as a stop that adds to the journey time. $$Total Time = \text{Driving Time} + (\text{Number of Stops} \times \text{Stop Duration})$$ ### Step-by-Step Solution 1. **Calculate Continuous Driving Time:** * Total Distance = $600$ km * Speed = $100$ km/hr * Driving Time = $\frac{600}{100} = 6$ hours. 2. **Calculate Number of Intermediate Stops:** * The train stops every $75$ km. * Total intervals = $\frac{600}{75} = 8$. * Since the 8th stop is the final destination, the number of intermediate stops is $8 - 1 = 7$. 3. **Calculate Total Stopping Time:** * Each stop lasts $3$ minutes. * Total stopping time = $7 \times 3 = 21$ minutes. 4. **Calculate Final Total Time:** * Total Time = $6$ hours + $21$ minutes = $6$ hrs $21$ min. ### Exam Strategy & Shortcut To quickly find the number of stops, divide the total distance by the stop interval distance. If the result is a whole number $N$, the number of stops is $N - 1$. If it has a remainder, the number of stops is the quotient. Here, $\frac{600}{75} = 8$ perfectly, so $8 - 1 = 7$ stops. ### Common Pitfall Forgetting to subtract $1$ from the total number of stops when the distance is perfectly divisible by the interval. Including the destination as a "stop" would erroneously yield $24$ minutes of stopping time. ### Final Answer Therefore, the correct answer is **6 hrs 21 min**.