Question

Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

Answer 1

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

Case I: When Abdul travels 300 Km by train and the 200 Km by taxi

Time taken by Abdul to travel 300 Km by train =

Time taken by Abdul to travel 200 Km by taxi =

Total time taken by Abdul to cover 500 Km =

It is given that total time taken in 5 hours 30 minutes

Case II: When Abdul travels 260 Km by train and the 240 km by taxi

Time taken by Abdul to travel 260 Km by train =

Time taken by Abdul to travel 240 Km by taxi =

In this case total time of the journey is 5 hours 36 minutes

Putting and, , the equations and reduces to

Multiplying equation by 6 the above system of equation becomes

Subtracting equation from we get

Putting in equation, we get

Now

and

Hence, the speed of the train is ,

The speed of the taxi is .