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Mr. Venkat takes a trip from Chennai to Bengaluru and back. While going his speed is $$40\ \text{km/hr}$$ half the way and $$60\ \text{km/hr}$$ for the remaining half of the distance. When he returns he drives at $$40\ \text{km/hr}$$ for half the time and at $$60\ \text{km/hr}$$ for the remaining half time of travel back. His average speed in the entire trip is
For equal distances the average speed going is $$\frac{2 \times 40 \times 60}{100} = 48$$ km/hr, and for equal times the average speed returning is $$\frac{40 + 60}{2} = 50$$ km/hr. If each way is D km, the total time is $$\frac{D}{48} + \frac{D}{50}$$. The overall average speed is $$\frac{2D}{\frac{D}{48} + \frac{D}{50}} = \frac{2 \times 2400}{98} \approx 48.98$$ km/hr.
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