Question

a journey of 192 km from a town a to town b takes 2 hours more by an ordinary train than a super-fast train .if faster train is 16 km/h more than find the speed of the ordinary train and faster train

Answer 1

$\huge\black{{Solution:-}}$

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