SOLUTION: If a tectonic plate is moving at the rate of 0.5cm/year, how long would it take to move 100 nautical miles? Conversion factors: 1nmi=2000 yards, 2.54cm=1 inch, 5280 feet=1 mile

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Question 370148: If a tectonic plate is moving at the rate of 0.5cm/year, how long would it take to move 100 nautical miles?
Conversion factors: 1nmi=2000 yards, 2.54cm=1 inch, 5280 feet=1 mile
Would you grid this and cancel out common units??? please help
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
I'm not sure what is meant by "grid this" but I'll try to help anyway.

For a problem like this you have the given ratio of 0.5cm/year and you have any conversion factors that you will need. These conversion factors can be represented as fractions. For example, 2.54cm = 1. If we divide both sides by 1 inch we get 2.54cm/1 inch = 1. If we divide both sides by 2.43cm instead we get 1 inch/2.54cm. And either way these fractions are 1's!

So we have the the original ratio (which can also be inverted) and all the different conversion factors. What we are going to do is figure out what product of these various fractions will give us the answer.

The answer to this problem is supposed to be years per nautical miles. For this we will need a fraction with years in the numerator and nautical miles in the denominator. We can get the years in the numerator by using the given ration upside down.
(1 year/0.5 cm)
For the nautical miles in the denominator we can use the conversion factor 1nmi = 2000yds with the nmi in the denominator:
(1 year/0.5 cm)*(2000 yards/1nmi)
At this point we have the units we want in the numerator and denominator. But we also have units we do not want. We need to find conversion factors that will allow us to cancel the unwanted units (the yards in the numerator and the centimeters in the denominator). To get rid of the centimeters we can use the conversion factor 2.54cm = 1 inch. Since the centimeters we want to cancel are in the denominator, we willuse the conversionfactor with the centimeters in the numerator:
(1 year/0.5 cm)*(2000 yards/1nmi)*(2.54cm/1 inch)
The centimeters now cancel out. But now we have inches in the denominator and we still have the yards in the numerator. A conversion factor (which was not provided) which will help with both! 1 yard = 36 inches. We want the inches on top (to cancel the inches we have on the bottom and we want the yards on the bottom to cancel the yards on top:
(1 year/0.5 cm)*(2000 yards/1nmi)*(2.54cm/1 inch)*(36 inches/1 yard)
If you look as what we have now, you should be able to see that all the units cancel each other out except for the years on top and the nmi on the bottom! SO all we need to do is multiply out the fractions:
years/nmi
which simplifies as follows:
(((182880/0.5}}} years/nmi
365760 years/nmi
This is how many years for 1 nmi. For 100 nmi:
100 nmi*(365760 years/nmi)
(Notice how the nmi's cancel.) This gives us:
36576000 years for 100 nautical miles.