Discussion
Myra cycles to a friend's house 5 km away to deliver a packet. She goes at a speed of 12 km/hour and returns at a speed of 8 km/h. Her average speed during the whole trip is -
Answer: B
Her average speed is 9.6 km/h.
Average speed is total distance divided by total time, not the average of the two speeds:
\[ \begin{aligned} t &= \frac{5}{12} + \frac{5}{8} = \frac{10 + 15}{24} = \frac{25}{24}\ \text{h} \\ v &= \frac{10}{25/24} = \frac{240}{25} = 9.6\ \text{km/h} \end{aligned} \]
For equal distances this is the harmonic mean, \(\frac{2 \times 12 \times 8}{12 + 8} = 9.6\). 10 km/h is the simple average of 12 and 8, the common mistake, because she spends longer at the slower speed. 20 km/h adds the speeds, and 5 m/s (18 km/h) is far too fast.
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