A man travels 50 km at a speed of 25 km/h, the next 40 km at 20 km/h and thereafter 90 km at 15 km/h. What is his average speed (in km/h) for the entire journey?

Introduction / Context:
This problem is a straightforward application of the concept of average speed over multiple segments of a journey with different speeds. Many students mistakenly average the given speeds directly, but the correct approach is always to use total distance divided by total time. Here, the man travels three segments of known distances at three different constant speeds, and we must compute his overall average speed for the complete trip.

Given Data / Assumptions:
- Segment 1 distance = 50 km, speed = 25 km/h.
- Segment 2 distance = 40 km, speed = 20 km/h.
- Segment 3 distance = 90 km, speed = 15 km/h.
- The man travels in a straight path and there are no breaks or waiting times between segments.
- Each speed is constant over its respective segment.

Concept / Approach:
Average speed for a complete journey is defined as:
average speed = total distance / total time.
It is never the simple arithmetic mean of the speeds, unless the time spent at each speed is exactly the same. In this problem, distances are different, so we must calculate the time taken for each leg using time = distance / speed, then sum these times to find the total time, and then divide the total distance by this total time.

Step-by-Step Solution:
Step 1: Compute the total distance travelled.Total distance = 50 + 40 + 90 = 180 km.Step 2: Compute time for each segment.Time for first 50 km = 50 / 25 = 2 hours.Time for next 40 km = 40 / 20 = 2 hours.Time for last 90 km = 90 / 15 = 6 hours.Step 3: Total time = 2 + 2 + 6 = 10 hours.Step 4: Average speed = total distance / total time = 180 / 10 = 18 km/h.

Verification / Alternative check:
You can check the result by noticing that the man spends most of his time at the lowest speed of 15 km/h (6 hours), so the overall average must be closer to 15 km/h than to 25 km/h. The value 18 km/h fits this intuition: it is slightly above 15 but well below 25. This qualitative check supports the calculated answer, confirming that the arithmetic was done correctly.

Why Other Options Are Wrong:
- 25 km/h is simply the first segment speed and is higher than any realistic average, given that later segments are slower.
- 20 km/h might look like a rough central value, but it ignores the longer time spent at 15 km/h and is not based on total distance and time.
- 15 km/h is the slowest segment speed; to get an average of 15 km/h, the man would need to travel at 15 km/h for the entire journey, which is not the case here.

Common Pitfalls:
The most common mistake is to compute (25 + 20 + 15) / 3 = 20 km/h and assume it is the average speed. This is incorrect because average speed is weighted by time (or distance), not by the number of speed values. Another error is forgetting to add all distances and times carefully, leading to arithmetic mistakes. Always follow the total distance over total time formula rigorously for mixed-speed journeys.

Final Answer:
The man’s average speed for the entire journey is 18 km/h.