AMC 8 1994 Problem 17

AMC8 1994 年第 17 题

数列与规律★★★☆☆

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

Pauline Bunyan 第一小时可以铲 20 立方码的雪，第二小时 19 立方码，第三小时 18 立方码，以此类推，每小时比前一小时少铲一立方码。如果她的车道宽 4 码、长 10 码，覆盖着 3 码深的雪，那么她铲完雪所需的小时数最接近

A.4
B.5
C.6
D.7
E.12

正确答案 · Correct Answer

解析 · Solution

Solution 1

Her driveway has (4)(10)(3)=120 cubic yards of snow. After the first hour she would have 120-20=100 cubic yards, then 100-19=81, 81-18=63, 63-17=46, 46-16=30, 30-15=15, and 15-14=1 cubic yard after the seventh hour. It will take her a little more than seven hours to shovel it clean, which is closest to

\text{(D)7}

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