An express train travels at an average speed of 100 km/h and stops for 4 minutes after every 75 km. How long does it take the train to reach a destination that is 600 km away from the starting point, including all stoppages?

Introduction / Context:
This question involves a train that travels with a given average running speed but includes regular stops. The goal is to compute the total journey time including these stoppages. Problems like this require careful calculation of both running time and stopping time and are common in aptitude tests dealing with practical applications of speed, distance, and time.

Given Data / Assumptions:

• Running speed of express train = 100 km/h.
• The train stops for 4 minutes after every 75 km traveled.
• Total distance to destination = 600 km.
• We assume no stop is counted after the final arrival at 600 km.
• Speeds between stops are constant.

Concept / Approach:
First, we compute the running time without considering stops by dividing the total distance by the running speed. Then we determine how many 75 km segments fit into 600 km and how many stops are made before the final destination. For each such segment (except after the final arrival), we add 4 minutes of stoppage time. The total time is the sum of running time and stoppage time, which is finally expressed in hours and minutes.

Step-by-Step Solution:
Running time without stops = total distance / speed = 600 / 100 = 6 hours. Number of 75 km segments in 600 km = 600 / 75 = 8. The train stops after each 75 km except after the final arrival. So number of stops = 8 - 1 = 7 stops. Stopping time per stop = 4 minutes. Total stopping time = 7 * 4 = 28 minutes. Total journey time = 6 hours running + 28 minutes stopping. Total time = 6 hours 28 minutes.

Verification / Alternative check:
We can check that the number of stops is correct by listing the points at which the train stops: after 75 km, 150 km, 225 km, 300 km, 375 km, 450 km, and 525 km. After reaching 600 km, the train has reached its destination and no further stop is needed for this calculation. There are indeed 7 intermediate stops, giving a total of 28 minutes stoppage time.

Why Other Options Are Wrong:
6 hours ignores the stoppage time completely. 6 hours 24 minutes and 6 hours 32 minutes correspond to fewer or more stops than actually occur. 7 hours 21 minutes is far too large and does not correspond to the given stopping pattern. Only 6 hours 28 minutes correctly accounts for 6 hours of running and 28 minutes of stoppage time.

Common Pitfalls:
Some students count a stop after the final 600 km segment, leading to 8 stops instead of 7. Others divide 600 by 75 incorrectly or forget to convert 4 minutes to a fraction of an hour when working entirely in hours. Carefully counting intermediate stops and handling units consistently avoids these mistakes.

Final Answer:
The express train takes 6 hours 28 minutes to reach the destination, including all stops.