Question

A man travels 600 km partly by train and partly by car. If the covers 400 km by train and the rest by car, it takes him 6 hours 30 minutes. But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

Answer 1

Let the speed of the train be x km/hr that of the car be y km/hr, we have the following cases:

Case I: When a man travels 600Km by train and the rest by car

Time taken by a man to travel 400 Km by train =

Time taken by a man to travel (600-400) =200Km by car =hrs

Total time taken by a man to cover 600Km =

It is given that total time taken in 8 hours

Case II: When a man travels 200Km by train and the rest by car

Time taken by a man to travel 200 Km by train =

Time taken by a man to travel (600-200) = 400 Km by car

In this case, total time of the journey in 6 hours 30 minutes + 30 minutes that is 7 hours,

...(ii)

Putting and, , the equations and reduces to

Multiplying equation (iii) by 6 the above system of equation becomes

Substituting equation and, we get

Putting in equation, we get

Now

and

Hence, the speed of the train is,

The speed of the car is.