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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

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. ganeshie8
    • one year ago
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    Hey! still here ?

  3. anonymous
    • one year ago
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    yes

  4. ganeshie8
    • one year ago
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    First of all, notice that the total journey has taken \(1\) hour.

  5. ganeshie8
    • one year ago
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    total time of journey = `forward time of journey` + `return time of journey`

  6. ganeshie8
    • one year ago
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    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
    • one year ago
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    similarly, the `return time of journey` is given by \(\dfrac{1~ km}{(x+1) ~km/hr}\)

  8. ganeshie8
    • one year ago
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    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
    • one year ago
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    Got it. Thank you so much @ganeshie8 :)

  10. ganeshie8
    • one year ago
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    np :) btw, \(x\) is the speed of car, not the distance travelled by car

  11. ganeshie8
    • one year ago
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    you will need to mulltiply \(x\) by the total time of journey to get the distance travelled

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

  13. anonymous
    • one year ago
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    which will be x2-2x + 1x - 1 = 0

  14. ganeshie8
    • one year ago
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    \(x^2 - 2x - 1 = 0\) we could simply use quadritic formula..

  15. anonymous
    • one year ago
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    Okay.

  16. thomas5267
    • one year ago
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    Is the distance travelled by the car independent of its velocity? I couldn't think straight now.

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