AMC8 2023

AMC8 2023 · Q11

AMC8 2023 · Q11. It mainly tests Rates (speed), Rounding & estimation.

NASA’s Perseverance Rover was launched on July $30,$ $2020.$ After traveling $292{,}526{,}838$ miles, it landed on Mars in Jezero Crater about $6.5$ months later. Which of the following is closest to the Rover’s average interplanetary speed in miles per hour?

NASA的Perseverance漫游车于2020年7月$30,$日发射。在飞行$292{,}526{,}838$英里后，它在大约$6.5$个月后登陆火星的Jezero陨石坑。以下哪项最接近漫游车的平均行星际速度（英里/小时）？

(A) \ 6{,}000 \ 6{,}000

(B) \ 12{,}000 \ 12{,}000

(D) \ 120{,}000 \ 120{,}000

(E) \ 600{,}000 \ 600{,}000

Answer

Correct choice: (C)

正确答案：（C）

Solution

Note that $6.5$ months is approximately $6.5\cdot30\cdot24$ hours. Therefore, the speed (in miles per hour) is \[\frac{292{,}526{,}838}{6.5\cdot30\cdot24} \approx \frac{300{,}000{,}000}{6.5\cdot30\cdot24} = \frac{10{,}000{,}000}{6.5\cdot24} \approx \frac{10{,}000{,}000}{6.4\cdot25} = \frac{10{,}000{,}000}{160} = 62500 \approx \boxed{\textbf{(C)}\ 60{,}000}.\] As the answer choices are far apart from each other, we can ensure that the approximation is correct.

注意到$6.5$个月大约是$6.5\cdot30\cdot24$小时。因此，速度（英里/小时）为 \[\frac{292{,}526{,}838}{6.5\cdot30\cdot24} \approx \frac{300{,}000{,}000}{6.5\cdot30\cdot24} = \frac{10{,}000{,}000}{6.5\cdot24} \approx \frac{10{,}000{,}000}{6.4\cdot25} = \frac{10{,}000{,}000}{160} = 62500 \approx \boxed{\textbf{(C)}\ 60{,}000}.\] 由于答案选项之间差距很大，我们可以确保这个近似值是正确的。

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