Consider the following statement:
A car journey consists of two parts. In the first part, the average speed is $u \mathrm {~km} / \mathrm { h }$. In the second part, the average speed is $v \mathrm {~km} / \mathrm { h }$. Hence the average speed for the whole journey is $\frac { 1 } { 2 } ( u + v ) \mathrm { km } / \mathrm { h }$.
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 $50 \mathrm {~km} / \mathrm { h }$ for 100 km . In the second part of the journey, the car travels at a constant speed of $40 \mathrm {~km} / \mathrm { h }$ for 100 km .
II In the first part of the journey, the car travels at a constant speed of $50 \mathrm {~km} / \mathrm { h }$ for one hour. In the second part of the journey, the car travels at a constant speed of $40 \mathrm {~km} / \mathrm { h }$ for one hour.
III In the first part of the journey, the car travels at a constant speed of $50 \mathrm {~km} / \mathrm { h }$ for 80 km . In the second part of the journey, the car travels at a constant speed of $40 \mathrm {~km} / \mathrm { h }$ for 100 km .