Wednesday, May 19, 2010

Special Guest: Sanjoy Mahajan

We here at Diary of Numbers love all things estimation.  For this reason, we consider a special honor that today’s question comes from Sanjoy Mahajan.  Dr. Mahajan is the Associate Director at the Teaching and Learning Laboratory at MIT and is also the author of Street-Fighting Mathematics, The Art of Educated Guessing and Opportunistic Problem Solving.  Dr. Mahajan would like to know,

“How much oil does the US import (in barrels/year)?”

Note: This should be an easy answer to look up, but as Dr. Mahajan notes, it is “an interesting question to find methods that don't require looking up anything.”  See if you can solve this without looking up anything.

Answer:  Per Dr. Mahajan’s request, I did not look up any figures for this calculation.  (I did, however, look up a conversion factor from “barrels” to “gallons.”)  To simplify the calculation, I assumed that the volume of oil imported is roughly equivalent to volume of gasoline used by cars.  Oil is used in applications aside of cars, but not all gasoline comes from imported oil, so I'll assume these two effects cancel each other.  I’ll further assume the average American fills up on gas about 2 times per week and he pays about $25 per fill up. Since gas is about $3 per gallon, we can compute the total amount oil each person consumes each week,

oil consumed = (# of fill ups) · (cost per fill up) / (cost per gallon)
= (2 fill ups per week per person) · ($25 per fill up) / ($3 per gallon)
= 17 gallons per week per person.

That’s about 0.40 barrels per week for each American.  There are about 300 million Americans.  From this, we can estimate the total number of barrels imported each year,

barrels per year = (barrels per week per person) · (# of people) · (# of weeks per year)
= (0.40 barrels per week per person) · (3.0×106 people) · (52 weeks per year)
= 6.2×109 barrels imported per year.

That’s an estimate of 6.2 billion barrels per year.  According to the U.S. Energy Information Administration, the U.S. imports 9,783,000 barrels/day, which is equivalent to 3.6 billion gallons per year.  Our estimate is off by less than a factor of 2.  This is partly due to luck, but it’s also due to the power of the Fermi estimation.  Thanks for a great question, Dr. Mahajan. 

You can order a copy of Dr. Mahajan’s Street-Fighting Mathematics on Amazon.

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