So, total time taken-time spent in train+time spent in car=250/x+120/y
but,total time of journey is 4 hours, so

250/x + 120/y
250/x + 120/y = 4
125/x + 60/y = 2

Again, when he travels 130 km by train and the rest by car
Time taken by him to travel 130 km by train = 130/x hrs
Time taken by him to travel 240 km (370-130) by car = 240/y
Total time taken = = 130/x + 240/y hrs

But, it is given that the time of journey is 4 hrs 18 min i.e., 4 18/66 * hrs = 4 3/10 * hrs

So. 130/x + 240/y = 43/10 (2)

Substitute 1/x = a_{i} and 1/y = b in equations (1) and (2)

125a + 60b = 2
130a + 240b = 43/10

For 60 and 240, LCM is 240. Using the elimination method

Equation (3)×4 500a +240b=8

Equation (3)×4 130a + 240b = 43/10 (Same sign, so subtract)

370a = 8 - 43/10 = (80 - 43)/10 = 37/10