A car drives without changing direction. For the first 2 hours its average speed is 60 km/h and for the next 3 hours it is 40 km/h. Find the average speed over the whole 5 hours.

Step-by-step solution

1. 1

   Recognise that the times are given, not the distances. When two segments last different amounts of time, the correct average is the time-weighted mean, so we build total distance first.

2. 2

   Find each segment distance. $s_1=60\times 2=120\text{ km},\qquad s_2=40\times 3=120\text{ km}$

3. 3

   Add distances and times. $s=120+120=240\text{ km},\qquad t=2+3=5\text{ h}$

4. 4

   Divide. $v_{tb}=\frac{240}{5}=48\text{ km/h}$

5. 5

   Reject the naive mean. The plain average $\tfrac{60+40}{2}=50\text{ km/h}$ (option A) would only be right if the two speeds were held for equal times. Here the slower speed lasts longer, so the true average is pulled down to $48\text{ km/h}$, option B.