Excluding stoppages, a train runs at 108 km/h; including stoppages, its average speed is 90 km/h. For how many minutes does the train stop per hour?

Introduction / Context:A train’s “running speed” excludes stoppages, while the “average speed” includes them. Comparing distances covered in one hour gives the fraction of time actually spent moving versus stopping.

Given Data / Assumptions:

• Running speed = 108 km/h
• Average speed (with stops) = 90 km/h
• Consider a 1-hour window.

Concept / Approach:In 1 hour of clock time, distance covered = 90 km. If the train had run the whole hour, it would have covered 108 km. Therefore, the “running time” = distance/run speed = 90/108 hours. The remainder of the hour is stoppage time.

Step-by-Step Solution:

Verification / Alternative check:In 50 minutes of running (5/6 h), distance = 108 * 5/6 = 90 km, matching the average of 90 km/h over the full hour.

Why Other Options Are Wrong:

• 5, 6, 9 minutes do not produce 90 km in one clock hour at 108 km/h running speed.

Common Pitfalls:

• Confusing average speed with running speed.
• Not standardizing to a 60-minute window.

Final Answer:10