Question

a man travels 600km partly by traiin and partly by car. if he travels 400km by train and the rest by car, it takes him 6 hours and 30 mins. but if he travels 200km by train and the rest by car , he takes 1/2 n' hour longer. find the speed of the train and that of the car.

Answer 1

Let speed of train be x km/hr and car be y km/hr
Total distance=600km
CASE 1 
Distance travelled by train=400km
Distance travelled by car  =600-400=200km
Time taken by train = D/S=400/x
Time taken by car   = D/S=200/y
CASE 2
Distance travelled by train=200km
Distance travelled by car  =600-200=400km
Time taken by train = D/S=200/x
Time taken by car   = D/S=400/y
A.T.Q
400 + 200 = 6+30
  x        y          60
Let 1/x and 1/y be a and b
400a+200b=13/2
200a+100b=13/4..........(i)
AND 
200 + 400 = 7
 x        y  
Let 1/x and 1/y be a and b
200a+400b=7......(ii)
In (i) & (ii)using elimination method
  200a+100b=13/4
+200a+400b=+7 
-         -            -       
-300b=-15/4
b=-15/4*-300
b=1/80
and Putting in (ii) we get
200a=7-400(1/80)
a=2/200
a=1/100
NOW a=1/x and b=1/y 
so x=>Speed of train=>100 km/hr
and y=>Speed of car=>80km/hr

Hope it helps