2008 AMC 12B Problems/Problem 6

Problem 6

Postman Pete has a pedometer to count his steps. The pedometer records up to $99999$ steps, then flips over to $00000$ on the next step. Pete plans to determine his mileage for a year. On January $1$ Pete sets the pedometer to $00000$ . During the year, the pedometer flips from $99999$ to $00000$ forty-four times. On December $31$ the pedometer reads $50000$ . Pete takes $1800$ steps per mile. Which of the following is closest to the number of miles Pete walked during the year?

$\textbf{(A)}\ 2500 \qquad \textbf{(B)}\ 3000 \qquad \textbf{(C)}\ 3500 \qquad \textbf{(D)}\ 4000 \qquad \textbf{(E)}\ 4500$

Solution

Every time the pedometer flips, Pete has walked $100,000$ miles. Therefore, Pete has walked a total of $100,000 * 44 + 50,000 = 4,450,000$ steps, which is $4,450,000/1,800 = 2472.2$ miles, which is closest to answer choice A.

2008 AMC 12B (Problems • Answer Key • Resources)
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2008 AMC 12B Problems/Problem 6

Problem 6

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