Question

Pauline Bunyan 第一小时可以铲 $20$ 立方码雪，第二小时铲 $19$ 立方码，第三小时铲 $18$ 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 $4$ 码、长 $10$ 码，并被 $3$ 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 $20$ cubic yards for the first hour, $19$ cubic yards for the second, $18$ for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is $4$ yards wide, $10$ yards long, and covered with snow $3$ yards deep, then the number of hours it will take her to shovel it clean is closest to

$4$

$5$

$6$

$7$

$12$

答案：D

知识点：体积等差数列

难度评级：1000

小提示：

先求雪的总体积： $4 \times 10 \times 3$ 立方码

First find the total volume of snow: $4 \times 10 \times 3$

大提示：

逐小时累加 $20 + 19 + 18 + \cdots$ ，直到累计量达到雪的体积

Add $20 + 19 + 18 + \cdots$ hour by hour until the running total reaches the volume

解答：

雪的体积是 $4 \times 10 \times 3 = 120$ 立方码。

累计铲雪量是 $20 + 19 + 18 + 17$ $+ 16 + 15 + 14 = 119$ 立方码，也就是 $7$ 小时的工作量。第八小时的铲雪速度是每小时 $13$ 立方码，因此剩下的一立方码需要 $\dfrac{1}{13}$ 小时。准确时间是 $7\dfrac{1}{13}$ 小时，最接近 $7$ 小时。

所以正确答案是 D。

The volume of snow is $4 \times 10 \times 3 = 120$ cubic yards.

The amounts shoveled add up to $20 + 19 + 18 + 17$ $+ 16 + 15 + 14 = 119$ after $7$ hours. In the eighth hour her rate is $13$ cubic yards per hour, so the last cubic yard takes $\dfrac{1}{13}$ hour. The exact time is therefore $7\dfrac{1}{13}$ hours, which is closest to $7$ .

Thus, the correct answer is D .

1994 AMC 8 第 17 题

答案：D

难度评级：1000

小提示：

大提示：

解答：

其他年份的第 17 题