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Thread: It seems simple but I am struggling with this.

  1. #1 It seems simple but I am struggling with this. 
    Forum Radioactive Isotope
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    Ok John cycles from Norwich to London at 15 mph .
    The distance is 100 miles.

    Geraldine takes the car and ,at a steady speed of 45 mph leaves at the same time as John .
    She arrives in London ahead of John ,turns around instantly and follows the same back path to Norwich.

    She meets John en route.

    How long after John has left Norwich does he encounter Geraldine?

    Especially what is the formula for getting the answer.

    And what is the formula if all we know is that Geraldine's speed is "r" times faster than John's?

    thanks!


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  3. #2  
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    Its pretty trivial, let be the distance form london to the point the two meet, be Geraldine's speed and be John's. so we can say:



    Now multiply it by witch yeilds:

    Now let be so

    Solving this for gives us:

    is the answer (time after leaving Norwich)

    Good luck!


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  4. #3  
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    A good way to figure this out would be to consider the distances traveled by Geraldine and John. John will be traveling x, while geraldine will be traveling 200-x, since she will be traveling a full 100 miles (the distance from Norwich to London) and then the difference of johns position along the 100 mile track. Geraldine is traveling at , while John is traveling at

    Now, we know that the times for travel will be the same, so all that's left is determine the distances traveled relative to eachother. We will call time c, so and also and since we know the times equal eachother, we can equate the two expressions.



    If we know the speeds, or atleast that one speed is a specific fraction of the other speed, we can solve for x. Let's say the specific fraction is A. Now we have
    Last edited by Arcane_Mathematician; February 1st, 2014 at 08:31 PM.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  5. #4  
    Moderator Moderator Janus's Avatar
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    Even more trival:

    The Sum of the distances traveled by Geraldine and John is 2d ( if d is the distance from London to Norwich)

    The sum of their speeds is V1+V2.

    Ergo, the Time it takes for them to meet is



    If v2 is 3*v1, then



    Last edited by Janus; February 1st, 2014 at 09:47 PM.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  6. #5  
    Forum Radioactive Isotope
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    thanks all .I was rustier than I thought!
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