A motorist travels from one place to another 150 km away at an average speed of 50 km/h and returns along the same route at an average speed of 30 km/h. What is his average speed for the entire round trip in km/h?

Introduction / Context:
This question deals with average speed over a round trip where the speeds for the two legs of the journey are different. It highlights that the average speed for the entire trip is not the simple arithmetic mean when the distances are the same but the times differ.

Given Data / Assumptions:
- Distance one way = 150 km.
- Speed going = 50 km/h.
- Speed returning = 30 km/h.
- The route and distance are identical in both directions.
- We need the average speed for the total distance travelled.

Concept / Approach:
The general formula for average speed over multiple segments is:
Average speed = (Total distance) / (Total time)
Because the distances in the two directions are equal, we can either use this formula directly or apply the harmonic mean formula for speeds over equal distances.

Step-by-Step Solution:
Step 1: Distance each way = 150 km, so total distance = 150 + 150 = 300 km.Step 2: Time taken going = Distance / Speed = 150 / 50 = 3 hours.Step 3: Time taken returning = 150 / 30 = 5 hours.Step 4: Total time = 3 + 5 = 8 hours.Step 5: Average speed for round trip = Total distance / Total time = 300 / 8 km/h.Step 6: Compute 300 / 8 = 37.5 km/h.

Verification / Alternative check:
For equal distances with speeds u and v, the average speed can be written as:
Average speed = (2 * u * v) / (u + v)
Here, u = 50 and v = 30:
Average speed = 2 * 50 * 30 / (50 + 30) = 3000 / 80 = 37.5 km/h.
This matches the result obtained from distance and time directly.

Why Other Options Are Wrong:
- 35 and 36 km/h are lower than the true average and would require more than 8 hours for 300 km, which contradicts the computed times.
- 38.2 km/h is higher than 37.5 km/h and does not correspond to the actual total time of 8 hours.

Common Pitfalls:
- Taking the simple average (50 + 30) / 2 = 40 km/h, which is incorrect because time spent at each speed differs.
- Mixing up total distance with one way distance when applying the formula.
- Rounding too early and miscalculating the final value.

Final Answer:
The average speed for the entire journey is 37.5 km/h.