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Math Help - Word problem

  1. #1
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    Word problem

    A train, x meters long, traveling at a constant speed, takes 20 seconds from the time if first enters a tunnel 300 meters long until the time it completely emerges from the tunnel. One of the stationary ceiling lights in the tunnel is directly above the train for 10 seconds. Find X.


    I would really appreciate it if someone could give me a step by step explanation.

    Thanks

    Vicky.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Vicky1997 View Post
    A train, x meters long, traveling at a constant speed, takes 20 seconds from the time if first enters a tunnel 300 meters long until the time it completely emerges from the tunnel. One of the stationary ceiling lights in the tunnel is directly above the train for 10 seconds. Find X.


    I would really appreciate it if someone could give me a step by step explanation.

    Thanks

    Vicky.
    If the train is traveling at a constant rate, then the ratio of distance to time will be the same over any distance and respective time interval. So, we can set up a proportion

    \frac{300+x}{20}=\frac{x}{10}

    Where 300+x represents the distance the train traveled through the 300 meter long tunnel plus its own length.

    Since the light is small enough to be considered as a single point, we don't need to consider its length.
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  3. #3
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    Thanks.
    I understand it now but I'm not sure I will be able to do similar problems on my own yet.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Vicky1997 View Post
    Thanks.
    I understand it now but I'm not sure I will be able to do similar problems on my own yet.
    Problem solving is what its all about. Getting good at it takes time but really pays off. The most important things to do when you look at a problem are

    1. Write down what's given
    2. write down what you wish to find.
    3. Figure out how the quantities are related.

    In my opinion, it is number three that is the hardest. Practice makes perfect.

    In your case, the fact that the speed was constant was a clue. It tells you that the two quantities (distance and time) are relate by the simple physical concept

    Speed=\frac{distance}{time}

    best of luck!

    DEUCE!
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