<p>So, good try to those who tried to arrive at a mathematical answer. To those who only responded with arguments, consider English and communications as future college majors. Maybe you become a lawyer and can convince the physicists that rocks actually fall up.</p>
<p>There are no “unknown” variables to this problem, despite the laments of some. After all, in the real world, one must use real world information to solve real world questions.</p>
<p>The Problem was:</p>
<p>How thick is the layer that comes off a car’s tire in one revolution in normal use?</p>
<p>The Answer is: (Do not scroll down if you are still working on solving it):</p>
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As I hinted earlier, one can easily solve the problem if one treats the tire like a roll of toilet paper. Like a roll of toilet paper unrolling, a tire in use on a road is leaving some of its rubber on the road as the tire runs on the road, just like rolling a roll of toilet paper on a surface. The tire has a center which will not come off, like a toilet paper’s carboard core. Although the toilet paper roll and the tire appear not to reduce in size, of course, they do. At some point, all that is left is the toilet paper core, and on the tire, the tread disappears and your mechanic tells you that you need to replace your tires. So, as the tire is driven on the road, a layer of tire rubber is deposited on the road (because it sticks to the road, or whatever, the cause does not matter for this problem, nor is the cause important to solve the problem). Ever notice on concrete highways that the places in the lanes where the tires run is darker than in the center of the lane?</p>
<p>So now to the very simple math.</p>
<p>How long is the deposit of rubber on the road: A tire lasts about 50,000 miles = 5 x 10^4 miles = (5 x 10^4 miles) (1.6 x 10^3 meters/mile) meters = 10^8 meters</p>
<p>What is the circumference of the tire: pi x D = 3 x (0.5 meters) = 1.5 meters</p>
<p>How many times did the tire revolve: 10^8 / 1.5 = 10^8 times</p>
<p>Thickness of the tire tread: 1 centimeter = 10^-2 meters</p>
<p>Thickness of the deposited rubber layer: 10^-2 / 10^8 = 10^-10 meters</p>
<p>10^-10 meters is about the size of an average large molecule.</p>
<p>The final answer: the thickness of the rubber layer deposited is: one molecule.</p>
<p>A molecule is a concept that many people can readily understand. And by solving this problem, one gets some idea of how to relate small numbers to physical objects.</p>
<p>Again, when I was at MIT, I think no one in the entire freshman physics class of 300+ got the correct answer. So if you didn’t, you are on par with class average. But solving this problem, or at least seeing how it is solved, teaches you how to think in different ways.</p>
<p>Good luck, future math geeks. And remember that all math is founded on reality or devised to explain reality. Keep it real (except for i 
).</p>