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A journey of 192 km between two cities take 2 hours less by a fast train than by a slow train. If the average speed of the slow train is 16 km/hr less than that of the fast train, the average speed of the fast train is :

A journey of 192 km between two cities take 2 hours less by a fast train than by a slow train. If the average speed of the slow train is 16 km/hr less than that of the fast train, the average speed of the fast train is : Correct Answer 48 km/hr

Let the speed of the fast train be x km/hr
Then, speed of the slow train = (x - 16) km/hr
$$\eqalign{ & \therefore \frac{{192}}{{x - 16}} - \frac{{192}}{x} = 2 \cr & \Rightarrow \frac{1}{{x - 16}} - \frac{1}{x} = \frac{1}{{96}} \cr & \Rightarrow {x^2} - 16x - 1536 = 0 \cr & \Rightarrow \left( {x - 48} \right)\left( {x + 32} \right) = 0 \cr & \Rightarrow x = 48\,\text{km/hr} \cr} $$

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