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Thread: river crossing

  1. #1
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    Default river crossing

    Two polluting carbon emitting gas guzzling power boats start at the same time from opposite side of the polluted Marrickville River, that is not ebbing or flowing, being full of garbage.

    They travel at constant speed at rights angles to the river banks, but one is faster than the other.
    They pass at a point 720 metres from the nearest shore.
    Both boats remain at the wharf for 10 minutes while they fill with more polluting petroleum before starting back.
    On the return trip, they met 400 metres from the other shore.
    Once the reach the shore again, they are stoned to death by green Councillors.

    How wide is the river?

    Greg

  2. #2
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    Default

    Does it matter? Their dead!

  3. #3
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  4. #4
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    Default sorry.

    Try this:
    Let x be the river width.
    On the first trip the ratios of distances travelled by the 2 boats is x-720:720

    On the second trip it is:

  5. #5
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    Default

    2x - 400 : x + 400

    .....
    Visit my website at www.myFineWoodWork.com

  6. #6
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    Default And

    Those ratios are equal.


    x-720/720 = 2x-400/x+400

    (x-720)(x+400) = 720(2x-400)

    x2-720x+400x-288000 = 1440x-288000

    x2-320x-1440x = 0

    x(x-1760) = 0

    So the answer is:


    Thanks

    Greg

    ps x2 is x 'squared', I can't make the machine type the correct symbol

  7. #7
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    Default

    You already gave the answer, it's 'x'

  8. #8
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    Default

    After 15 minutes or so trying to remember how to solve these, I instead remembered that I hate maths so instead went and looked at pretty tools I can't afford. I'm feeling much better about not knowing the answer now!
    ---

    Visit my blog The Woodwork Geek to see what I've been up to or follow my ramblings on Twitter

  9. #9
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    Default

    1760m
    Visit my website at www.myFineWoodWork.com

  10. #10
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    Default

    I was a bit worried about the 10min stop by the boats but as it turned out it didn't matter in the end.
    Visit my website at www.myFineWoodWork.com

  11. #11
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    Default

    Let x be the width
    Let v1 be the velocity faster boat
    Let v2 be the velocity slower boat
    Let T be the time taken

    The boats first meet:
    v1/v2 = (x - 720) / 720

    Second meet:

    v1 = (2x - 400) / (T - 10)
    v2 = (x + 400) / (T - 10)

    v1/v2 = (2x - 400) / (x + 400)

    Therefore (x - 720) / 720 = (2x - 400) / (x + 400)

    x = 1760
    Visit my website at www.myFineWoodWork.com

  12. #12
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    Default yards

    When this was first mooted, it was in yards, and as we know who are post 1963...

    1760 yards equals..... 1........

    Good work Scott ( as usual...).

    Greg

  13. #13
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    Default

    1760 yards is a mile. Easy!!

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