Calculating the Atlantic Ocean's Widening: A Plate Tectonics Question

[globetrotter269]

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!

 

[drpizza]

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 $$\frac{1 foot}{12 inches}$$ or you could multiply by $$\frac{12 inches}{1 foot}$$

So, if I was changing 3cm/hour to something else, (I intentionally changed it a little bit), I could do this:
$$\frac{3 cm}{1 hour}*\frac{1 meter}{100 cm}$$
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 $$\frac{1 meter}{100 cm}$$ is equal to 1. The resulting units from this operation will be
$$\frac{3}{1 hour}*\frac{1 meter}{100}$$ 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:

$$\frac{3 cm}{1 hour}*\frac{1 meter}{100 cm}*\frac{1 kilometer}{1000 meters}*\frac{1 hour}{60 minutes}. . .$$

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.

 

[globetrotter269]

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?

 

[calcnd]

Well, are there 100 cm per km or 100,000?

I'd set it up like this, anyways.

$$\frac{change in distance}{change in time}$$

$$=\frac{\Delta d}{\Delta t}$$

$$\frac{3 cm}{year} = \frac{\Delta d}{\Delta t}$$

$${\Delta t} = \frac{\Delta d}{3 \frac{cm}{year}}$$