**1st case** :

distance travelled by train = 300km

and 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

hence solved................