anonymous one year ago A mail train and a car starts its journey at the same time, parallel to each other in the same direction. The car starts its journey from the rear end of the train. The car reached the front end of the train and come back to the back end of the train. In the mean time, the mail train travels a distance of 1 km. If the speed and the length of mail train in 1 kmph and 1 km respectively, then how much distance does car travel ? 1) 2 km 2) 1 + root 2 km 3) 2 + root 2 km

1. anonymous

@ganeshie8

2. ganeshie8

Hey! still here ?

3. anonymous

yes

4. ganeshie8

First of all, notice that the total journey has taken $$1$$ hour.

5. ganeshie8

total time of journey = forward time of journey + return time of journey

6. ganeshie8

Let $$x$$ be the speed of car, when the car is going in the same direction as train, the relative velocity is $$x-1$$. since the train is $$1$$km long, the forward time of journey is given by $$\dfrac{1~ km}{(x-1) ~km/hr}$$

7. ganeshie8

similarly, the return time of journey is given by $$\dfrac{1~ km}{(x+1) ~km/hr}$$

8. ganeshie8

since the total time of journey is $$1$$ hr, we have : $\dfrac{1}{x-1}+\frac{1}{x+1}=1$ solve $$x$$, the speed of car.

9. anonymous

Got it. Thank you so much @ganeshie8 :)

10. ganeshie8

np :) btw, $$x$$ is the speed of car, not the distance travelled by car

11. ganeshie8

you will need to mulltiply $$x$$ by the total time of journey to get the distance travelled

12. anonymous

Yes. However, I am not able to split the equation as it is coming out as x2 - 2x -1 = 0

13. anonymous

which will be x2-2x + 1x - 1 = 0

14. ganeshie8

$$x^2 - 2x - 1 = 0$$ we could simply use quadritic formula..

15. anonymous

Okay.

16. thomas5267

Is the distance travelled by the car independent of its velocity? I couldn't think straight now.