An express train travels at an average speed of 100 km/hr and stops for 3 minutes after every 75 km. How much time does it take to reach its destination, which is 600 km away from the starting point?

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Accepted Answer

To calculate the total time taken by the train to travel 600 km, we first determine the time required to cover the distance without stoppages.

The train travels at an average speed of 100 km/hr. Therefore, the time taken to cover 600 km is:  
$$
	ext{Time taken} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{600}{100} = 6 \, 	ext{hours}.
$$

Next, calculate the number of stoppages during the journey. The train stops for every 75 km traveled. Since the total distance is 600 km:  
$$
	ext{Number of stoppages} = \frac{	ext{Total distance}}{	ext{Distance per stop}} - 1 = \frac{600}{75} - 1 = 8 - 1 = 7.
$$

Each stoppage lasts for 3 minutes. Therefore, the total time spent during stoppages is:  
$$
	ext{Total stoppage time} = 	ext{Number of stoppages} 	imes 	ext{Stoppage duration} = 7 	imes 3 = 21 \, 	ext{minutes}.
$$

Convert the stoppage time into hours:  
$$
	ext{Stoppage time in hours} = \frac{	ext{Total stoppage time}}{60} = \frac{21}{60} = 0.35 \, 	ext{hours}.
$$

Finally, add the travel time and stoppage time to find the total time taken:  
$$
	ext{Total time taken} = 	ext{Travel time} + 	ext{Stoppage time in hours} = 6 + 0.35 = 6.35 \, 	ext{hours}.
$$

Convert this into hours and minutes:  
$$
6.35 \, 	ext{hours} = 6 \, 	ext{hours and} (0.35 	imes 60) = 21 \, 	ext{minutes}.
$$

Thus, the total time taken by the train is **6 hours and 21 minutes**.

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