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# Christmas Math 101

How long does Santa have to hang out when he's dropping presents off at your house? And how fast do his reindeer fly? Keep on reading to find out about the incredible math behind Santa's magical night!

By
Jason Marshall, PhD,
December 23, 2013
Episode #179

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## How Fast Do Santa's Reindeer Fly?

This time crunch leads to another great Christmas math 101 question: How fast do Santa's reindeer need to fly? While this seems like a tough question to answer, remember that we're really just looking to come up with a quick and dirty estimate—so we shouldn't be afraid to use our trusty mathematical intuition and to make reasonable simplifying assumptions.

That's about 1,250 miles per second. Pretty zippy! In fact, it's several thousand times the speed of sound! Those are some mighty impressive reindeer.

For example, to answer this question we need to come up with a rough estimate of the average distance between the 92 million houses that Santa visits. To do so, let's simplify the situation and make the assumption that each of these 92 million houses are spaced equally across the entire Earth. Obviously this isn't actually true since there are oceans, mountain ranges, and lots of other obstacles in the way. But it is a reasonable first approximation for us to begin with.

According to WolframAlpha, the Earth's surface area is about 200 million square miles. Each of the 92 million houses that Santa delivers to therefore occupies a patch of Earth that's 200,000,000 square miles / 92,000,000 or approximately 2.2 square miles in size. In other words, if you divide the Earth up into a bunch of 2.2 square mile patches, each patch would contain an average of 1 house that Santa delivers to. If we take the square root of 2.2, we find that the length of the side of this patch—which is also the rough distance between houses—is approximately 1.5 miles.

So how fast do Santa's reindeer have to fly? Well, if each of those 92 million houses are an average of 1.5 miles apart, Santa has to travel 92 million x 1.5 miles = 138 million miles! As we've seen, if Santa uses Earth's rotation to his advantage, he has up to 31 hours of darkness for his journey. So if he and his reindeer travel 138 million miles over the course of these 31 hours, they'll be moving at a very brisk average speed of 138 million miles / 31 hours = 4.5 million miles per hour.

That's about 1,250 miles per second. Pretty zippy! In fact, it's several thousand times the speed of sound! Those are some mighty impressive reindeer indeed.

## Wrap Up

Okay, that's all the math we have time for today.

Please be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Happy holidays and thanks for reading, math fans!

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Calculator gift image courtesy of Shutterstock.

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