A boat goes a certain distance at 30 km/h and returns the same distance at 20 km/h. What is the average speed (in km/h) for the entire journey?

Introduction / Context:
Here we deal with average speed over a round trip. The boat travels the same distance twice but at different speeds: faster one way and slower on the way back. The average speed is not the simple average of 30 and 20.

Given Data / Assumptions:
• Speed going out = 30 km/h.• Speed coming back = 20 km/h.• Distances in both directions are equal.

Concept / Approach:
Average speed is defined as total distance divided by total time. When the distance each way is the same, we can either compute it directly or use the harmonic mean formula for two speeds: average speed = (2uv) / (u + v), where u and v are the two speeds.

Step-by-Step Solution (distance–time method):
Step 1: Let the one-way distance be D km.Step 2: Time for onward journey = D ÷ 30 hours.Step 3: Time for return journey = D ÷ 20 hours.Step 4: Total distance = 2D.Step 5: Total time = D/30 + D/20 = (2D + 3D) ÷ 60 = 5D ÷ 60 = D/12 hours.Step 6: Average speed = total distance ÷ total time = 2D ÷ (D/12) = 2D × (12/D) = 24 km/h.

Verification / Harmonic mean check:
Using the formula: average = (2uv) / (u + v) = 2 × 30 × 20 ÷ (30 + 20) = 1200 ÷ 50 = 24 km/h, which matches the result obtained earlier.

Why Other Options Are Wrong:
25 or 24.5 or 25.5: These are close to the arithmetic mean (25), but average speed for equal distances must be the harmonic mean, which is always less than or equal to the arithmetic mean when speeds differ.

Common Pitfalls:
A common error is to simply average the two speeds: (30 + 20) ÷ 2 = 25 km/h. This ignores the fact that more time is spent at the slower speed, pulling the overall average down.

Final Answer:
The average speed for the entire journey is 24 km/h.