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Math Help - Distance problem

  1. #1
    Raj
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    Distance problem

    Two trains, one starting at Point A and the other at Point B, travel toward one another.
    Train #1 travels at 140km/h towards Point B, while Train #2 travels at 120km/h towards Point A.
    If the trains begin at the same time, Point A and Point B are 285km apart, how far from Point A will the trains pass each other.

    I'm not sure what to find here in order to answer the probelm, any help please
    Last edited by Raj; February 1st 2008 at 05:47 AM.
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  2. #2
    Super Member wingless's Avatar
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    Follow these steps:

    1- When will the trains pass each other? Find it, we can call this time t.

    2- How far will Train 1 go in time t ?
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Raj View Post
    Two trains, one starting at Point A and the other at Point B, travel toward one another.
    Train #1 travels at 140km/h towards Point B, while Train #2 travels at 120km/h towards Point A.
    If the trains begin at the same time, Point A and Point B are 285km apart, how far from Point A will the trains pass each other.

    I'm not sure what to find here in order to answer the probelm, any help please
    For Train 1 we can say the following:

    v = 140

    For Train 2:

    v = 120


    We know Dist. = velocity x time

    So the distance that T_{1} travels is 140t

    For T_{2} the distance is 120t

    There will be a certain time when 285km (or miles) minus the distance that T_{1} has traveled is equal to the distance that T_{2} has traveled.

    So we can therefore say: 285 - 140t = 120t

    Solving for t:

    t = \frac{57}{52}

    Dist_{T1} = 140 \left( \frac{57}{52} \right) = 153,462


    EDIT: I'm thinking I should be studying for a physicist ...
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  4. #4
    Super Member wingless's Avatar
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    Or you could say that their relative velocity is 140 + 120 = 260 km/h.

    V = \frac{x}{t}

    t = \frac{x}{V}

    t = \frac{285}{260} = \frac{57}{52}

    (140)(\frac{57}{52}) \approx 153.5 \text{ km}
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by wingless View Post
    Or you could say that their relative velocity is 140 + 120 = 260 km/h.
    I didn't even think it would be correct to say that... but it works out anyway.
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  6. #6
    Super Member wingless's Avatar
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    Quote Originally Posted by janvdl View Post
    I didn't even think it would be correct to say that... but it works out anyway.
    Why not?

    Just try to imagine the scene. Two trains are 285 km away and they're going to each other. When you look at them while you stand outside the trains, on the ground, you see that one of them (Train 1) is going at 140 km/h and the other one is traveling at 120 km/h.

    Now try to imagine it as you're in Train 1. You look at the other train and see that it's 285 km away and coming closer at 260 km/h. Now it's a simple calculation because your train is not moving but the other train does. It would pass you in 285/260 hours.

    I hope that was helpful
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  7. #7
    Raj
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    Quote Originally Posted by wingless View Post

    Now try to imagine it as you're in Train 1. You look at the other train and see that it's 285 km away and coming closer at 260 km/h. Now it's a simple calculation because your train is not moving but the other train does. It would pass you in 285/260 hours.

    I hope that was helpful
    Thats a great way of thinking about it, thanks
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