A car drove half the distance at 60 km/h and the rest at 40 km/h. Average speed?

Step-by-step solution

1. 1

   Step 1. Average speed is not the arithmetic mean

   Average speed = total distance / total time: $v_{av} = \dfrac{S}{t}$. Simply taking $(60+40)/2 = 50$ is WRONG here — the halves are halves of the distance, not of the time.

2. 2

   Step 2. Denote the distance

   Let the whole distance be $S = 2d$ (so $d$ for each half). The time for the first half is $t_1 = \dfrac{d}{60}$, for the second $t_2 = \dfrac{d}{40}$.