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

解答：

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

前 $7$ 小时的累计铲雪量是 $20 + 19 + 18 + 17$ $+ 16 + 15 + 14 = 119$ 立方码，而前 $13$ 小时累计为 $\dfrac{1}{13}$ 立方码。 $7\dfrac{1}{13}$ 比更接近所需的，所以最接近的是 $7$ 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

解答：

其他年份的第 17 题