Sunday, October 17, 2010

Special Guest Natalie Angier

Today we're pleased to have a question from special guest Natalie Angier.  Ms. Angier is a Pulitzer-prize winning science journalist for the New York Times.  She has authored several books, most recently, The Canon: A Whirligig Tour of the Beautiful Basics of Science.  She writes, "How many leaves are raked up nationwide on an average weekend afternoon in October?"

Before I begin, I have leaf-raking riddle for you.  Without adding or rearranging the words, add punctuation to the following sentence to make it grammatically correct: "A boy raking leaves." The answer is below.

If you're going to rake leaves, you need leaves to rake.  Some states like Arizona are desert-y and won't have many leaves to rake, but most places in the U.S. will have trees that shed.  Even if you live in the right climate, you still need a yard with at least one tree in it.  I'll assume that 1 out of 10 people owns a yard with a tree in it, since it's very likely that the actual number is greater than 1 out of 100 and less than 1 out of 1.  Of these people, some will rake, but many will use a leaf blower or just let the leaves lie.  Using a similar order-of-magnitude argument to the previous one, I'll assume 1 out of 10 people who have leaves rake them.  The average leaf raker might rake his/her leaves once in October, and there are about 8 good leaf-raking October weekend afternoons each year.  There are 3.1×108 people in the United States.   Combining these assumptions, we can estimate that,

# of people raking = (3.1×108 people) · (0.1 tree owners per person)
· (0.1 raker per tree owner)· (0.125 chance of raking now)
= 390,000 people raking leaves each weekend afternoon in October.

But the question specifically asked for the number of leaves raked.  This will clearly depend on the number of leaves a person has in his/her backyard.  According to at least one source, a mature tree can have up to 200,000 leaves.  To confirm this, I looked at leaves strewn across Tappan Square in Oberlin.  The mean separation was about 6 inches between leaves.  If you spread them out over a reasonably sized lawn (about 1/5 of an acre), you get about 200,000 leaves.  If each raker rakes this many leaves one a weekend, there will be,

# of leaves = (200,000 leaves per raker) · (390,000 raker)
= 7.8×1010 leaves raked.

That's 78 billion leaves raked nationwide each afternoon in October.  Thanks for the great question, Ms. Angier! 

For those wondering about my earlier grammatical riddle, the correct answer is "A boy, raking, leaves."

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