1. **State the problem:** Lee cycles 60 km at 30 km/h and returns the same 60 km at 20 km/h. We need to find the average speed for the entire journey. 2. **Formula for average speed:** Average speed for a round trip when speeds differ is given by the harmonic mean formula: $$\text{Average speed} = \frac{2 \times v_1 \times v_2}{v_1 + v_2}$$ where $v_1$ and $v_2$ are the speeds for the two parts of the journey. 3. **Calculate average speed:** Given $v_1 = 30$ km/h and $v_2 = 20$ km/h, $$\text{Average speed} = \frac{2 \times 30 \times 20}{30 + 20} = \frac{1200}{50} = 24 \text{ km/h}$$ 4. **Explanation:** The average speed is not the simple average because the time spent at each speed differs. Using the harmonic mean accounts for the different durations at each speed. **Final answer:** Lee's average speed for the whole journey is $24$ km/h.