1994 AMC 8 第 17 题

先试着解答 1994 AMC 8 第 17 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1994 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

17.

Pauline Bunyan 第一小时可以铲 2020 立方码雪,第二小时铲 1919 立方码,第三小时铲 1818 立方码,依此类推,每小时都比上一小时少铲一立方码。如果她的车道宽 44 码、长 1010 码,并被 33 码深的雪覆盖,那么她铲干净大约需要多少小时?
Pauline Bunyan can shovel snow at the rate of 2020 cubic yards for the first hour, 1919 cubic yards for the second, 1818 for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is 44 yards wide, 1010 yards long, and covered with snow 33 yards deep, then the number of hours it will take her to shovel it clean is closest to
44
55
66
77
1212
答案:D
知识点:体积等差数列
小提示:
先求雪的总体积:4×10×34 \times 10 \times 3 立方码
First find the total volume of snow: 4×10×34 \times 10 \times 3
大提示:
逐小时累加 20+19+18+⋯20 + 19 + 18 + \cdots,直到累计量达到雪的体积
Add 20+19+18+⋯20 + 19 + 18 + \cdots hour by hour until the running total reaches the volume
解答:
雪的体积是 4×10×3=1204 \times 10 \times 3 = 120 立方码。
累计铲雪量是 20+19+18+1720 + 19 + 18 + 17 +16+15+14=119+ 16 + 15 + 14 = 119 立方码,也就是 77 小时的工作量。第八小时的铲雪速度是每小时 1313 立方码,因此剩下的一立方码需要 113\dfrac{1}{13} 小时。准确时间是 71137\dfrac{1}{13} 小时,最接近 77 小时。
所以正确答案是 D。
The volume of snow is 4×10×3=1204 \times 10 \times 3 = 120 cubic yards.
The amounts shoveled add up to 20+19+18+1720 + 19 + 18 + 17 +16+15+14=119+ 16 + 15 + 14 = 119 after 77 hours. In the eighth hour her rate is 1313 cubic yards per hour, so the last cubic yard takes 113\dfrac{1}{13} hour. The exact time is therefore 71137\dfrac{1}{13} hours, which is closest to 77.
Thus, the correct answer is D .
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