Solution:

Concept: Average speed is total distance divided by total time. Let total distance be \( D \). Time for first half: \( t_1 = \frac{D/2}{v_1} \). Time for second half: \( t_2 = \frac{D/2}{v_2} \). Total time \( T = t_1 + t_2 = D \left( \frac{v_1 + v_2}{2v_1 v_2} \right) \). Average speed \( = \frac{D}{T} = \frac{2v_1 v_2}{v_1 + v_2} \).