A train crosses a stationary pole in 3 minutes. It crosses a 600 meter long platform in 5 minutes. What are the length and the speed of the train?

let the length of the train be x meters

speed of the train = $$\frac{train length}{time taken}$$ = $$\frac{x}{3}$$

speed of the train when train crosses the platform =  $$\frac{train length + platform length}{time taken}$$ = $$\frac{x+600}{5}$$

equating both  ($$\because$$ speed of the train is same)

 $$\frac{x}{3}$$ = $$\frac{x+600}{5}$$ 

5x = 3x + 1800 

2x = 1800 , x = 900 meters

speed of the train =  $$\frac{x}{3}$$ ( substituting value of x) 

$$\frac{900}{3\times 60 }$$ = 5 m/s ($$\because$$ 1 minute = 60 seconds)

converting it into km/h

$$5\times\frac{18}{5}$$ = 18 km/h