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Thread: Speed of Current

  1. #1
    Member harpazo's Avatar
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    Speed of Current

    A motorboat can keep a constant speed of 16 mph relative to the water. The boat makea a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?

    Let c = speed of current

    I know that 20 minutes is 20/60 of an hour or 1/3 of an hour.
    I also know that 15 minutes is 15/60 of an hour or 1/4 of an hour.

    The formula D = rt is often used in such questions. I also think the formula must somehow be manipulated to show what we are looking for.

    D = rt

    Upstream = c + 16

    Downstream = c - 16

    I stuck here.
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    Re: Speed of Current

    (@ 16-c).........................................>1/3

    1/4<..............................................@( 16+c)

    1/3(16 - c) = 1/4(16 + c)

    HOKAY?
    Next step I'd multiply the whole shebang by 12: 4(16 - c) = 3(16 + c) ...no more fractions!
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  3. #3
    Member harpazo's Avatar
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    Re: Speed of Current

    4(16 - c) = 3(16 + c)

    64 - 4c = 48 + 3c

    64 - 48 = 3c + 4c

    16 = 7c

    16/7 = c

    2.2857142857 = c

    2.29 mph = speed of current
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    Re: Speed of Current

    Yep. Usually better to leave as 16/7 = speed of current...

    Also, you can check yourself if correct by substituting in original:
    4(16 - c) = 3(16 + c)
    4(16 - 16/7) = 3(16 + 16/7) ????
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  5. #5
    Member harpazo's Avatar
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    Re: Speed of Current

    I did not know that speed can be expressed as fractions.
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    Cool Re: Speed of Current

    Everything is a fraction: 5 = 5/1
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    Re: Speed of Current

    Quote Originally Posted by DenisB View Post
    Everything is a fraction: 5 = 5/1
    Interesting. A lot of students do not know this fact. If a represents any number, then a/1 = any number as well because a divided by 1 = a or any number.
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