In the 1989 Loma Prieta earthquake in California, approximately 2 million books fell off the shelves at the Stanford University library. If you were the library administrator and wanted to hire enough part-time student labor to put the books back on the shelves in order in 2 weeks, how many students would you have to hire? (You may assume that the books just fell off the shelves and got a bit mixed up but books in different aisles did NOT get shuffled together.)

Solution

To do this estimate, we have to estimate 2 numbers: How long does it take to put a book back on the shelf, and how much time is each student going to work? Suppose that the books didn't get totally mixed -- they just fell from the shelves so they are near to where they belong. A worker then only has to pick them up, check the place compared to nearby books and put them on the shelf. I think a plausible number is 1 book every 5 seconds or 20 books/minute = 1200 books/hour. This might be a bit high, depending on how the books fell. I will estimate a reasonable rate to be 800 books/hour. If a part-time student is working 10 hours/week, in the two week period, each student can pick up about 800 x 20 = 16,000 books. We will therefore need 2,000,000 / 16,000 = 125 students working very hard if we want to make our deadline.

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