Problem:
Pauline Bunyan can shovel snow at the rate of cubic yards for the first hour, cubic yards for the second, for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is yards wide, yards long, and covered with snow yards deep, then the number of hours it will take her to shovel it clean is closest to
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The volume of the snow on the driveway is cubic yards. Adding the rates for consecutive hours yields , while consecutive hours yields . The -hour solution is closest to cubic yards.
The volume of the snow on the driveway is cubic yards. Computing the amount left after each hour, we have:
Since is closer to zero than is , the -hour solution is closest to cubic yards.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions