Question

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

Answer 1

@ganeshie8

Answer 2

Hey! still here ?

Answer 3

yes

Answer 4

First of all, notice that the total journey has taken \(1\) hour.

Answer 5

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

Answer 6

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 \(\dfrac{1~ km}{(x-1) ~km/hr}\)

Answer 7

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

Answer 8

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.

Answer 9

Got it. Thank you so much @ganeshie8 :)

Answer 10

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

Answer 11

you will need to mulltiply \(x\) by the total time of journey to get the distance travelled

Answer 12

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

Answer 13

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

Answer 14

\(x^2 - 2x - 1 = 0\)

we could simply use quadritic formula..

Answer 15

Okay.

Answer 16

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