Discussion
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Answer: B
Each half of the journey is \( \tfrac{D}{2} \) km.
\[ \frac{D/2}{21} + \frac{D/2}{24} = 10 \]
\[ \frac{D}{42} + \frac{D}{48} = \frac{8D + 7D}{336} = \frac{15D}{336} \]
\[ \frac{15D}{336} = 10 \quad\Longrightarrow\quad D = 224 \text{ km} \]
Equivalently, the average speed is the harmonic mean \( \tfrac{2 \times 21 \times 24}{45} = 22.4 \) kmph, and \( 22.4 \times 10 = 224 \).
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