Question

A man travels 600km partly by train and partly by car.If he covers 120km by train and rest by car ; it takes him 8 hours.But if he travels 200km by train and and by car ; he takes 20 minutes longer.Find the speed of the train and that of the car.

Answer 1

speed of train ---- t km/h
speed of car ----- c km/h

120/t + 480/c = 8
15/t + 60/c = 1
times tc
tc = 15c + 60t

200/t + 400/c = 25/3
times tc
(25/3)tc = 200c + 400t
tc = (3/25)(200c + 400t) = 24c + 48t

24c + 48 = 15c + 60t
9c = 12t
c = 4t/3

sub into 15/t + 60/c = 1
15/t + 60/(4t/3) = 1
15/t + 45/t = 1
t = 60 , then
c = 4(60)/3 = 80

the car's speed is 80 km/h, the train's is 60 km/h

check my arithmetic

Answer 2

Thanks :)