Question

Jack travelled 300 km by train and 200 km by taking 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

1st case

distance travelled by train = 300km

                      by taxi = 200km

    

          Let speed of train be x km/hr    

and  

  that of taxi be y km/hr.

                   

      so, time taken by train = d/s                        time taken by taxi = d/s

                                       = 300/x                                                = 200/y

  total time taken = 5hrs 30 mins = 5 1/2 hrs

                                  

           so, 300/x +200/y = 5 1/2 by solving we get : 600y + 400x = 11xy..........1

2nd case :

           

            distance travelled by train = 260 km          and by taxi = 240 km

           

     here also speed of train be x km/hr and of taxi be y km/hr

 

 Then time = d/s

          train time= 260/x hr                            of taxi = 240/y hr

        combiningly,total  time =

 

                             260/x + 240/y = 5hrs 36 mins

                       =>  or 260/x + 240/y = 5 3/5   on solving we get,

   

                      1300y + 1200x = 28xy...............2

eq 1 × 3 = 1800y + 1200x = 33xy

 

 on solving 1 and 2 we get:

         x=100 km/hr

        y= 80 km/hr