Discussion
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Answer: C
Average speed is total distance over total time, which for two equal legs is the harmonic mean, not the arithmetic one:
\[ \bar{v} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \]
The two legs are equal in distance, so
\[ \bar{v} = \frac{2 \times 64 \times 80}{64 + 80} = \frac{10240}{144} = 71.11 \text{ km/hr} \]
The arithmetic mean of 72 is close but slightly high. The 35.55 option is exactly half the right answer - the result of dividing by the total distance instead of one leg.
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