A 600 km journey takes 8 hours if 120 km is by train and the rest by car. It takes 20 minutes more if 200 km is by train and the rest by car. What is the ratio of train speed to car speed?

Let train speed = v_t and car speed = v_c. Write total time as a sum of segment times.

Step-by-step calculation
Case 1: 120/v_t + 480/v_c = 8  …(i)Case 2: 200/v_t + 400/v_c = 8 + 20/60 = 25/3  …(ii)Solve (i) and (ii):
Multiply (i) by 5 and (ii) by 6 to eliminate denominators conveniently:
(i) → 600/v_t + 2400/v_c = 40(ii) → 1200/v_t + 2400/v_c = 50Subtract the first from the second:
600/v_t = 10 ⇒ v_t = 60 km/hBack-substitute in (i):
120/60 + 480/v_c = 8 ⇒ 2 + 480/v_c = 8 ⇒ 480/v_c = 6 ⇒ v_c = 80 km/h

Final Answer
3:4 (train : car)