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The Car and the Train

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by nisagl750 » Wed Mar 07, 2012 9:11 am
A train and a car started at the same time ..... Car which was at rear end, reaches front end and comes back to rear end. In the mean time train travels 1 km. If the speed of the train is 1 km /hr ...wat is distance covered by car??

a) 1Km
b) 1/2Km
c) 1+sqrt(2) Km
d) 1-sqrt(2) Km

OA is
C
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by [email protected] » Wed Mar 07, 2012 7:43 pm
Let the length of the train=d and the speed of the car x km/hr.

The car travels from rear end to the front and to the rear end again. Total time elapsed=1 hr, since during this time the train has travelled 1 km.
Total time taken by the car=1
So, d/(x-1) + d/(x+1)=1 ( since from rear end to front end relative speed is x-1 and from front to rear end relative speed is x+1).
Solving we get x^2-2dx-1=0

Since the car travelled total 2d distance,then 2d=1km. Substituting this in the original equation we get,
x^2-2x-1=0
Solving we get, x=2+root(4+4)/2 or x=2-root(4+4)/2
Since x>0, x=2+root(4+4)/2
or x=1+root(2).

So the car har travelled x km(total time was 1 hour) i.e. 1+root(2) km.
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