22. A journey odjourney of 192 km from Mumbai to Pune takes 2 hours le

1.	22. A journey odjourney of 192 km from Mumbai to Pune takes 2 hours less by the fast train than by a slowain. If the average speed of the slow train is 16 km/hr less than that of the fast train, find theaverage speed of each train.
Answer» 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 = 2192/(x-16) - 192/x=2192x-192(x-16)/x(x-16)=23072=2x^2-32xx^2-16x-1536=0x²-48x+32x-1536=0x(x-48)+32(x-48)=0(x-48)(x+32)=0x= 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

22. A journey odjourney of 192 km from Mumbai to Pune takes 2 hours less by the fast train than by a slowain. If the average speed of the slow train is 16 km/hr less than that of the fast train, find theaverage speed of each train.

Answer»

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 = 2192/(x-16) - 192/x=2192x-192(x-16)/x(x-16)=23072=2x^2-32xx^2-16x-1536=0x²-48x+32x-1536=0x(x-48)+32(x-48)=0(x-48)(x+32)=0x= 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