Question

The journey of 192 km from Mumbai to Pune text 2 hours less by a superfast train then by an ordinary passenger train .if the average speed of the passenger train is 16 km / hour less than that of the super fast train determine their average speed.

Answer 1

Given, Total distance = 192 km

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

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

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

And, Time taken to cover 192 km by passenger 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, superfast train = 48 km/hr

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