A fast train takes 3 hours less than a slow train for a journey of 600 km.If the speed of the slow train is 10 km/h less than that of the fasttrain, find the speeds of the two trains.

By the given condition
Now fast train takes 3 hours less than a slow train.
i.e., slow train time - fast train time = 3
Therefore,

Multiplying both sides by x(x - 10) we get
3x(x -10)= 600x - 600(x-10)
3x ² - 30x = 600x - 600x + 6000
On rearranging we have
-3x ² + 30x + 600x - 600x + 6000 = 0
-3x ² + 30x + 6000 = 0 [Dividing throughout by 3]
-x ² + 10x + 2000 = 0
x ² - 10x - 2000 = 0
x ² - 50x + 40x - 2000 = 0
x(x - 50) + 40(x - 50) = 0
(x + 40)(x - 50) = 0
x + 40 = 0 or x - 50 = 0
x = - 40 or x = 50
Since the speed of the train cannot be negative.
Therefore we neglect the solution x = - 40.
Thus, the average speed of the fast train is 50 km/hr
and the average speed of the slow train is 40 km/hr.
Checking:

Thus, fast train takes 3 hours less for the journey and slow train speed is 10km/hr less than the fast train.