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Earth Science Quesetion

  1. Dec 14, 2006 #1
    Any help would be much appreciated with this problem.
    The problem is: The rate of plate movement along portions of the Mid-Atlantic Ridge has been determined to be 3 cm/yr. At this rate how long will it take the Atlantic Ocean to widen another one kilometer?

    I think what you need to do is first change the the 3 cm/yr into km/yr and then go from there. But I'm not sure how to do that and what to do after that.

    Thank's in advance!
     
  2. jcsd
  3. Dec 14, 2006 #2
    A technique that works well for converting one type of units to another is "multiply by one." When the numerator of a fraction is equal to the denominator, the value of the fraction is one. i.e. you can multiply by [tex]\frac{1 foot}{12 inches}[/tex] or you could multiply by [tex]\frac{12 inches}{1 foot}[/tex]

    So, if I was changing 3cm/hour to something else, (I intentionally changed it a little bit), I could do this:
    [tex]\frac{3 cm}{1 hour}*\frac{1 meter}{100 cm}[/tex]
    Note, when you're multiplying the fractions together, since you have the units cm in the numerator and in the denominator, you can cancel them out. The fraction [tex]\frac{1 meter}{100 cm}[/tex] is equal to 1. The resulting units from this operation will be
    [tex]\frac{3}{1 hour}*\frac{1 meter}{100}[/tex] Taking care of the number part, you have .03 and the units are meters/hour.

    You can do the entire conversion by taking the product of several conversion fractions (each with the numerator equal to the denominator; thus each time you're multiplying by one which results in an identical quantity although the number and units change) i.e. like this:

    [tex]\frac{3 cm}{1 hour}*\frac{1 meter}{100 cm}*\frac{1 kilometer}{1000 meters}*\frac{1 hour}{60 minutes}. . .[/tex]

    Note: the cm's cancel, then the meters cancel, resulting in kilometers. Then, the hours cancel, resulting in units of minutes. I realize that in your case, you'll probably want to leave the answer in terms of years, although you could convert to centuries.
     
    Last edited: Dec 14, 2006
  4. Dec 14, 2006 #3
    So, for my particular problem would the multiplication be:

    3 cm/1 yr x 1 km/100 cm?
    Resulting in an answer of 300 years?

    or, would it be 3 cm/1 yr x 1km/100,000 cm
    Resulting in an answer of 300,000 years?
     
    Last edited: Dec 14, 2006
  5. Dec 15, 2006 #4
    Well, are there 100 cm per km or 100,000?

    I'd set it up like this, anyways.

    [tex]\frac{change in distance}{change in time} [/tex]

    [tex]=\frac{\Delta d}{\Delta t}[/tex]

    [tex]\frac{3 cm}{year} = \frac{\Delta d}{\Delta t} [/tex]

    [tex] {\Delta t} = \frac{\Delta d}{3 \frac{cm}{year}}[/tex]
     
    Last edited: Dec 15, 2006
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