Question

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.

Answer 1

166.67 Km/hr = Speed of Train

11.63 Km/hr = Speed of car

Step-by-step explanation:

Let speed of train = x km/hr

Let speed of car = y km/hr

Total distance = 600 + 400 = 1000 Km.

Let 1/x = u and 1/y = v

Given:  

Distance / speed = time.

So 600/x + 400/y = 13/2

  2(600u + 400v) = 13

 1200u + 800v = 13 -------(1)

 200/x + 800/y = 7

 200u + 800v = 7 ------------(2)

Substracting (2) from (1), we get: 1000u = 6

therefore u = 6/1000

Substituting u in equation 2, we get 200(6/1000) + 800v = 7

12/10 +800v = 7

12 + 8000v = 700

8000v = 688

v = 688/8000

Therefore v = 86/1000

u = 1/x = 6/1000. Therefore x = 1000/6 = 166.67 Km/hr = Speed of Train.

v = 1/6 = 86/1000. Therefore y = 1000/86 = 11.63 Km/hr = Speed of car.