Question

A journey of 192 km between two cities takes 2 hours less by a fast train than by a slow train .If the average speed of the slow train is 16km/h less than that of a fast train .Find the average speed of each train

Answer 1

Given, Total distance = 192 km

Let the average speed of the faster train = x km/hr


So, average speed of the slower train = (x-16) km/hr

Now, Time taken to cover 192 km by faster train (t1)= 192/x

And, Time taken to cover 192 km by slower train (t2) = 192/(x-16)

According to question,

t2 - t1 = 2
192/(x-16) - 192/x=2
192x-192(x-16)/x(x-16)=2
3072=2x^2-32x
x^2-16x-1536=0
x²-48x+32x-1536=0
x(x-48)+32(x-48)=0
(x-48)(x+32)=0
x= 48 , -32

Speed can't be negative. So, x = 48 km/hr

Therefore, speed of faster train = 48 km/hr

And, speed of slower train = (48-16) = 32 km/hr