A boat goes upstream at 18 km/h and comes back downstream at 30 km/h over the same distance. What is the average speed (in km/h) for the entire journey?

Introduction / Context:
This is another average speed question over a round trip, now with upstream and downstream speeds given. The distance each way is the same, but the speeds differ, so we must use the definition of average speed or the harmonic mean formula.

Given Data / Assumptions:
• Upstream speed = 18 km/h.• Downstream speed = 30 km/h.• Distance upstream = distance downstream.

Concept / Approach:
Average speed = total distance ÷ total time. For equal distances at speeds u and v, the average speed is the harmonic mean: (2uv) ÷ (u + v). This accounts for the extra time spent travelling at the slower speed.

Step-by-Step Solution (harmonic mean):
Step 1: Let u = 18 km/h (upstream) and v = 30 km/h (downstream).Step 2: Average speed = (2uv) ÷ (u + v).Step 3: Substitute values: (2 × 18 × 30) ÷ (18 + 30) = (1080) ÷ 48.Step 4: 1080 ÷ 48 = 22.5 km/h.

Alternative distance–time method:
Step 1: Let one-way distance be D km.Step 2: Time upstream = D ÷ 18 hours.Step 3: Time downstream = D ÷ 30 hours.Step 4: Total distance = 2D.Step 5: Total time = D/18 + D/30 = (5D + 3D) ÷ 90 = 8D ÷ 90 = 4D/45 hours.Step 6: Average speed = 2D ÷ (4D/45) = 2D × 45 ÷ 4D = 90 ÷ 4 = 22.5 km/h.

Why Other Options Are Wrong:
24, 20.5, 25: These do not match the harmonic mean and arise from incorrect averaging or arithmetic mistakes.

Common Pitfalls:
The most frequent mistake is taking the simple average (18 + 30) ÷ 2 = 24 km/h, which ignores the unequal time spent at each speed. Always use total distance divided by total time, especially when dealing with different speeds over equal distances.

Final Answer:
The average speed for the entire journey is 22.5 km/h.