A train has to cover a distance of 900 km in 25 hours. What should be its average speed in metres per second?

Introduction / Context:
This problem is a straightforward application of the speed formula combined with unit conversion. Average speed is defined as total distance divided by total time. The twist is that the required answer must be in metres per second, while the distance and time are given in kilometres and hours. Converting units correctly is a critical skill for both exams and everyday use of measurements.

Given Data / Assumptions:

Distance to be covered = 900 km.
Total time allowed = 25 hours.
We want the average speed in metres per second (m/s).
Use 1 kilometre = 1000 metres, 1 hour = 3600 seconds.
We assume constant average speed over the entire journey.

Concept / Approach:
We first compute the average speed in km/h using speed = distance / time. Then we convert that speed to m/s by multiplying by 1000 / 3600, or equivalently by 5 / 18. Breaking the problem into these two clear steps avoids mixing units. Finally, we match the final numerical value with the correct option. A quick reasonableness check of the magnitude is also beneficial.

Step-by-Step Solution:
Step 1: Compute average speed in km/h. speed_kmph = 900 / 25 = 36 km/h. Step 2: Convert to m/s. speed_mps = 36 * 1000 / 3600. Calculate: 36 * 1000 = 36000. speed_mps = 36000 / 3600 = 10 m/s.

Verification / Alternative check:
We know 36 km/h is a classic reference speed that equals exactly 10 m/s because 36 * 5 / 18 equals 10. This known identity provides an immediate confirmation that the conversion is correct. Also, 900 km in 25 hours is a moderate train speed of 36 km/h, and 10 m/s is a realistic equivalent speed for a relatively slow passenger train or freight train.

Why Other Options Are Wrong:
Option c (18) and option d (36) would correspond to much higher speeds in km/h than 36 km/h if converted back, and thus do not match the original ratio of 900 km in 25 hours. Option a (20) is exactly double the correct value and may appear if someone mistakenly multiplies instead of dividing during conversion. Only 10 m/s exactly matches 36 km/h and fits all the given data.

Common Pitfalls:
Common errors include miscomputing 900 / 25, using 60 instead of 3600 when converting hours to seconds, or applying the 5 / 18 factor backwards (multiplying when one should divide, or vice versa). Carefully writing out each step with units and checking that the final units are m/s helps prevent such mistakes.

Final Answer:
The required average speed of the train is 10 m/s.