Question

2. A person travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car he takes 6 hours 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 car and that of the train.

Answer 1

Let the speed of train be 'x' km/hr && speed of car be 'y' km/hr
Given,
400/x + 200/y = 6 hrs 30 mins = 6 30/60 = 6 1/2 = 13/2 hrs...(i)
If he travels 200 km by train & rest by car he takes 30 mins more, that is, 7 hrs
200/x + 400/y = 7 hours......(ii)
(i)*2== 800/x + 400/y = 13..(iii)
(iii) - (ii)
800-200/x = 13-7
600/x = 6
x = 100 km/hr
sub value of 'x' in (ii)
200/100 + 400/y = 7
400/y = 7-2=5
y = 400/5 = 80 km/hr
Hence, Speed of train = 100 km/hr
Speed of car = 80 km/hr
Hope it helps.