TMUA 2018 Paper 2 Q3 — Worked Solution

P2·Logic & Quantifiers, Sequences & Series·5.5Official · 2018 · Q3

counterexampleaverage-speedweighted-mean

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

\frac{1}{2} (u + v) km/h

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

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

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

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