examday

/TMUA

Consider the following statement:

A car journey consists of two parts. In the first part, the average speed is $u$ km/h. In the second part, the average speed is $v$ km/h. Hence the average speed for the whole journey is $\frac12(u+v)$ 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 km/h for 100 km. In the second part of the journey, the car travels at a constant speed of 40 km/h for 100 km.
• II In the first part of the journey, the car travels at a constant speed of 50 km/h for one hour. In the second part of the journey, the car travels at a constant speed of 40 km/h for one hour.
• III In the first part of the journey, the car travels at a constant speed of 50 km/h for 80 km. In the second part of the journey, the car travels at a constant speed of 40 km/h for 100 km.