Question

An express train travelled at an average speed of 100 kmph, stopping for 3 minutes after every 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, then how many kilometres did the local train travel in the time it took the express train to travel 600 km?

• A. 307.5 km
• B. 900 km
• C. 1200 km
• D. 1000 km

Answer 1

The Correct Option is A

The correct option is (A): 307.5
Let's solve this step by step.
Explanation: For the Express Train:
- The express train travels at an average speed of 100 km/h.
- The express train stops for **3 minutes** (which is 0.05 hours) after every 75 km.
Now, let's calculate how much time the express train takes to cover 600 km.
1. Total Distance Covered: 600 km
2. Distance Between Stops: 75 km
3. Number of Stops:
  \[\frac{600}{75} - 1 = 8 - 1 = 7 \text{ stops} \quad (\text{since the last stop is after the final destination})\]
4. Time Spent Stopping: 
  \[7 \times 0.05 = 0.35 \text{ hours}\]
5. Time Spent Traveling: 
  \[\frac{600}{100} = 6 \text{ hours}\]
6. Total Time Taken by Express Train: 
  \[6 + 0.35 = 6.35 \text{ hours}\]
For the Local Train:
- The local train travels at 50 km/h.
- The local train stops for 1 minute (which is 0.0167 hours) after every 25 km.
Now, let's calculate how much distance the local train covers in 6.35 hours.
1. Distance Between Stops: 25 km
2. Number of Stops in 6.35 hours:
  \[\frac{50 \times 6.35}{25} - 1 = 12.7 - 1 = 11.7 \text{ stops}\]
  We'll round it to 11 stops.
3. Time Spent Stopping: 
  \[11 \times 0.0167 = 0.1837 \text{ hours}\]
4. Effective Travel Time: 
  \[6.35 - 0.1837 = 6.1663 \text{ hours}\]
5. Distance Traveled by Local Train:
  \[6.1663 \times 50 = 307.5 \text{ km}\]
Conclusion:
The local train travels 307.5 km in the time it takes the express train to travel 600 km.