Question 602452
Rohan travels 600 km from his home partly by train and partly by car. He takes eight hours if he travels 120 km by train and rest by car. he takes 20 minutes more if he travels 200 km by train and rest by car. find the speed of train and car.
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let x=speed of train
let y=speed of car
travel time=distance/speed
..
120/x+480/y=8
200/x+400/y=8+1/3=25/3
..
let u=1/x
let v=1/y
..
120u+480v=8
200u+400v=25/3
..
120u+480v=8
600u+1200v=25
..
600u+2400v=40 (multi. by 5)
600u+1200v=25
subtract
1200v=15
v=15/1200
y=1/v=1200/15=80
..
120u=8-480v=8-(480*15/1200)=8-6=2
u=2/120=1/x
x=120/2=60
.. 
ans:
speed of train=60 km/hr
speed of car=80 km/hr