Question

A journey of 192 km takes 2hr less by a fast train than by a slow train. If the avg spreed of the slow train be 16km less than of fast train what is the avg speed of the fastest train

Answer 1

Hy

Let the speed of the average passenger train be 'x' km/hr.
So, the time taken by the passenger train = 192/x.
So, the average speed of the super fast train = (x + 16) km/hr
So, the time taken by the super fast train = 192/(x + 16). 
Given : Time taken by the passenger train to travel 192 km - time taken by super fast train to cover the distance of 192 km = 2 hours.
Therefore,
192/x - 192/(x + 16) = 2   Taking L.C.M.. we get

192x + 3072 + 192x   
_______________   = 2
 x (x + 16)

3072/x(x + 16) = 2    After cross multiplying, we get
3072 = 2x² + 32x
2x² + 32x - 3072 = 0
Dividing it by 2, we get
x² + 16x - 1536 = 0 
x² + 48x - 32x - 1536 = 0
x(x + 48) - 32(x + 48) = 0
(x + 48) (x - 32) = 0
x = - 48 or x = 32
The speed of the train cannot be negative, therefore the speed of the passenger train is 32 km/hr
And the speed of the super fast train is 32 + 16 = 48 km/hr


It will help you .