To travel 708 km, an Express train takes 6 hours more than Rajdhani train. If however, the speed of the Express train is doubled, it takes 3 hours less than Rajdhani train. What is the speed of Rajdhani train?

Let speed of Rajdhani train = $$x$$ km/hr and Express train = $$y$$ km/hr

Using, time = distance/speed

Acc. to ques, => $$\frac{708}{y} - \frac{708}{x} = 6$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{6}{708} = \frac{1}{118}$$ ----------------(i)

If speed of express train is doubled = $$2y$$ km/hr

=> $$\frac{708}{x} - \frac{708}{2y} = 3$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{3}{708} = \frac{1}{236}$$ ----------------(ii)

Adding equations (i) and (ii), we get :

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{118} + \frac{1}{236}$$

=> $$\frac{1}{2y} = \frac{3}{236}$$

=> $$y = \frac{118}{3}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{3}{118} - \frac{1}{118}$$

=> $$\frac{1}{x} = \frac{2}{118} = \frac{1}{59}$$

=> $$x = 59$$ km/hr