crayon riddle 8th grade

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Rachel loves to color. One of her fat crayons wears down to nothing after 15 hours and her skinny crayon wears down to nothing after 6 hours.. One day she starts coloring at 10:30am with two crayons one fat one skinny with the same height. At what time will the skinny crayon be 1/2 height of fat crayon

  • crayon riddle 8th grade -

    The amount of crayon left is the original length-amount used.

    The amount used depends on time. Now if one assumes both were the same original length (not stated in problem), then

    lengthskinny=orglength-time*origlength/6

    lengthfat=origlength-time*origlength/15

    so if lenghtskinny=1/2 lengthfat, then

    1/2lengthfat=Lo(1-time/6) and
    lengthfat=Lo(1-time/15)

    I would divide the first equation by the second...
    1/2= (1-time/6)/(1-time/15)

    multiply both sides by 2(1-time/15)
    and it ought to solve quickly.
    Nice problem: compliments to the originator.

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