AMC 8 1994 Problem 17

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 $\text{(A)}\ 4 \text{(B)}\ 5 \text{(C)}\ 6 \text{(D)}\ 7 \text{(E)}\ 12$