Discussion
A car travels half the distance with a velocity of 20 kmh-1 and another half distance with a velocity of 30 kmh-1 along a straight road. The average velocity of the car in km h-1 is
Answer: E
The average velocity is 24 km h-1.
For equal distances \(d\) at speeds \(v_{1}\) and \(v_{2}\), the average is total distance over total time:
\[ \begin{aligned} \bar{v} &= \frac{2d}{\frac{d}{v_{1}} + \frac{d}{v_{2}}} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \\ &= \frac{2 \times 20 \times 30}{50} = 24 \end{aligned} \]
The trap is the arithmetic mean, 25 km h-1. The car spends longer at the slower speed, so the true average, the harmonic mean, is lower than 25.
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