AMC12 2008 B

AMC12 2008 B · Q6

AMC12 2008 B · Q6. It mainly tests Rates (speed), Rounding & estimation.

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?

邮递员 Pete 有一个计步器来记录他的步数。计步器最多记录到 $99999$ 步，然后在下一步翻转到 $00000$。Pete 计划计算他一年的里程数。1 月 $1$ 日 Pete 将计步器设为 $00000$。在这一年中，计步器从 $99999$ 翻转到 $00000$ 共四十四次。12 月 $31$ 日计步器显示 $50000$。Pete 每英里走 $1800$ 步。以下哪个最接近 Pete 这一年走的英里数？

(A) 2500 2500

(B) 3000 3000

(D) 4000 4000

(E) 4500 4500

Answer

Correct choice: (A)

正确答案：（A）

Solution

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

计步器每翻转一次，Pete 就走了 $100,000$ 步。因此 Pete 一共走了 $100,000 \cdot 44 + 50,000 = 4,450,000$ 步，换算成英里为 $4,450,000/1,800 = 2472.2$ 英里，最接近选项 $\boxed{A}$。

Topics