Discussion
Rohit covers one-fourth of the total distance at 20 km/hr, one-fourth at 10 km/h and rest of his journey at 80 km/h. Find Rohit’s average speed for the whole distance?
Answer: A
Take the total distance as \( D \) and add the three times.
\[ t = \frac{D/4}{20} + \frac{D/4}{10} + \frac{D/2}{80} = \frac{D}{80} + \frac{D}{40} + \frac{D}{160} \]
\[ = \frac{2D + 4D + D}{160} = \frac{7D}{160} \]
\[ \bar{v} = \frac{D}{7D/160} = \frac{160}{7} = 22.85 \text{ km/hr} \]
Averaging the three speeds would give \( \tfrac{110}{3} = 36.7 \) km/hr, far too high - the slow 10 km/hr leg dominates the total time even though it covers only a quarter of the distance.
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