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A car travels between places A and B covering first $$\frac{1}{3}$$ of the distance at $$25\text{ kmph}$$ and the remaining distance at $$40\text{ kmph}$$ for some time and $$60\text{ kmph}$$ for an equal amount of time. Find the average speed (in kmph) of the car.
Correct Answer: 37.5
Let $$AB = 3d$$. The first $$d$$ takes $$\frac{d}{25}$$. For the remaining $$2d$$, equal times $$t$$ at 40 and 60 give $$100t = 2d$$, so the time is $$2t = \frac{d}{25}$$. Total time $$= \frac{2d}{25}$$, so the average speed is $$\frac{3d}{2d/25} = 37.5\text{ kmph}$$.
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