Consider the following statement:

A car journey consists of two parts. In the first part, the average speed is $u\text{ km/h}$. In the second part, the average speed is $v\text{ km/h}$. Hence the average speed for the whole journey is $\frac{1}{2}(u+v)\text{ km/h}$.

Which of the following examples of car journeys provide(s) a counterexample to the statement?

I In the first part of the journey, the car travels at a constant speed of $50\text{ km/h}$ for $100\text{ km}$. In the second part of the journey, the car travels at a constant speed of $40\text{ km/h}$ for $100\text{ km}$.

II In the first part of the journey, the car travels at a constant speed of $50\text{ km/h}$ for one hour. In the second part of the journey, the car travels at a constant speed of $40\text{ km/h}$ for one hour.

III In the first part of the journey, the car travels at a constant speed of $50\text{ km/h}$ for $80\text{ km}$. In the second part of the journey, the car travels at a constant speed of $40\text{ km/h}$ for $100\text{ km}$.