A man travelling in a train counts 41 telephone posts passing by in one minute. The posts are known to be spaced 50 metres apart along the track. At what speed (in km/h) is the train travelling?

Introduction / Context:
This is a classic speed estimation question where an observer counts equally spaced objects along the track, such as telephone posts. By relating the number of posts, the distance between them, and the time taken, we can work out the speed of the train. The important detail is how to convert the counted posts into actual distance travelled.

Given Data / Assumptions:

- The man counts 41 telephone posts in 1 minute.
- Distance between consecutive telephone posts = 50 metres.
- The train moves at a constant speed along a straight track.
- Counting starts as the train is opposite one post and continues until the 41st post passes him.

Concept / Approach:
If there are n posts, there are n - 1 equal gaps between them. When the observer starts counting at one post and ends when the 41st post passes, the train has effectively travelled across 40 gaps between posts. We multiply the number of gaps by the spacing to get distance, then divide by time to get speed in m/s, and finally convert to km/h.

Step-by-Step Solution:
Number of posts counted = 41. Number of gaps between them = 41 - 1 = 40. Distance between posts = 50 m. Total distance travelled in 1 minute = 40 * 50 = 2000 m. Time taken = 1 minute = 60 seconds. Speed in m/s = distance / time = 2000 / 60 = 100 / 3 m/s. Convert to km/h: multiply by 18 / 5. Speed in km/h = (100 / 3) * 18 / 5 = (100 * 18) / (15) = 1800 / 15 = 120 km/h.

Verification / Alternative check:
We can do an approximate mental check: if the train travels about 2 km (2000 m) in one minute, then in 60 minutes it would travel about 120 km, giving a speed of around 120 km/h. This quick check confirms that our exact calculation of 120 km/h is reasonable and fits the values in the problem.

Why Other Options Are Wrong:
60 km/h: This would correspond to roughly 1 km in 1 minute, not 2 km, and would involve crossing far fewer posts.
100 km/h and 110 km/h: These values are lower than the correct speed and would imply fewer than 40 gaps of 50 m each in one minute, so they do not match the data.

Common Pitfalls:
Many students incorrectly multiply the number of posts by the spacing, using 41 * 50, without realising that the distance is determined by the gaps. Others forget to convert metres per second to kilometres per hour by using the factor 18 / 5, which leads to an answer in the wrong units. Being precise about gaps and unit conversion avoids these errors.

Final Answer:
The speed of the train is 120 km/h.