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Find the distance that the Earth travels in one day in its path around the Sun. Assume that a year has 365 days and that the path of the Earth around the Sun is a circle of radius 93 million miles.

I'm doing precalc review for a calc class and I don't know how to solve this.

Thanks in advance!

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Okay, if it takes 365 days to travel $2\pi\times 93\text{ million miles}$, then it takes 1 day to travel ______. Fill in the blank. (Hint: ratios) –  J. M. Sep 19 '11 at 1:54
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x/1 = (2pi * 93,000,000) / 365?? so x=1600921.188? –  KubaSub Sep 19 '11 at 2:11
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ratios are awesome! thanks :) –  KubaSub Sep 19 '11 at 2:14
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@J.M. You should post the hint as an answer. :) –  Srivatsan Sep 19 '11 at 2:16
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@Sri: Dunno, I'm thinking it might be a good idea for KubaSub to try to write his solution in his own words. (For instance, where did I get the $2\pi\times 93$ million miles? KubaSub should answer that himself, if he truly understood what I did there.) ;) –  J. M. Sep 19 '11 at 2:19
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2 Answers

The circumference of a circle of radius $r$ is $2\pi r$; you’ve been given $r$, so you can find the circumference of the orbit. It takes the Earth $365$ days to travel that distance, so in $1$ day it travels what fraction of the circumference?

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KubaSub should have remembered that he couldn't get rid of the one on a whim. The answer he should have left over is: x/1=1600921.188. Therefore, you will have to multiply both sides by x to get it by itself. Leaving: 1=1600921.188x. You then divide both sides by 1600921.188. The answer is: x = 6.2464 miles.

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You can remove the $1$ in the denominator "on a whim". Going from $x/1=1600921.188$ to $1=1600921.188x$ is incorrect. It would be fine if the left side of the first were $1/x$ instead. –  Ross Millikan Nov 6 '13 at 16:27
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