To find the total duration of the journey, we must break down the problem into two distinct components:
Running Time: The actual time taken by the train to cover the distance while in motion.
Stoppage Time: The total time spent stationary at periodic intervals along the route.
Total Time=Running Time+Stoppage Time
Step 1: Calculate the Running Time
The actual running time is calculated by dividing the total distance by the average speed of the train without considering the stoppages:
Total Distance=600 km
Speed=100 kmph
Running Time=SpeedTotal Distance
Running Time=100600=6 hours
Step 2: Calculate the Total Number of Stoppages
The train halts every 75 km. To find the number of halts across the full journey, we divide the total distance by the interval gap:
Number of Intervals=75600=8
Crucial Rule: The 8th halt occurs exactly at the 600th km mark, which is the final destination station. Since the train has reached its journey's end point, this final stop is not counted as an intermediary halt.
Therefore, we subtract 1 from the calculated intervals:
Total Number of Stoppages=8−1=7 stoppages
Step 3: Calculate the Stoppage Time
Each stoppage lasts for a duration of 3 minutes.
Total Stoppage Time=7×3 minutes=21 minutes
Step 4: Calculate Total Journey Duration
Adding both segments together gives us the absolute travel time:
Total Time=6 hours+21 minutes=6 hrs. 21 min.
Final Answer
The total time taken to reach the station is 6 hrs. 21 min.
Therefore, the correct option is (b).
