A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

Match the items on the right to the items on the left.

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

Let the speed of train be ‘a’ and speed of car be ‘b’.

Speed = distance/time

Given, man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes.

But, if he travels 200 km by train and the rest by car, he takes half an hour longer(eq2).

⇒ -600 = -6a
⇒ a = 100 km/hr

Thus, 4 + 200/b = 6.5
200/b = 6.5-4

⇒ 200/b = 2.5
⇒ 2.5b = 200
⇒ b = 80 km/hr