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

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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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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First of all, notice that the total journey has taken \(1\) hour.
total time of journey = `forward time of journey` + `return time of journey`
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 \(\dfrac{1~ km}{(x-1) ~km/hr}\)
similarly, the `return time of journey` is given by \(\dfrac{1~ km}{(x+1) ~km/hr}\)
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.
Got it. Thank you so much @ganeshie8 :)
np :) btw, \(x\) is the speed of car, not the distance travelled by car
you will need to mulltiply \(x\) by the total time of journey to get the distance travelled
Yes. However, I am not able to split the equation as it is coming out as x2 - 2x -1 = 0
which will be x2-2x + 1x - 1 = 0
\(x^2 - 2x - 1 = 0\) we could simply use quadritic formula..
Okay.
Is the distance travelled by the car independent of its velocity? I couldn't think straight now.

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