Difference between revisions of "1994 AJHSME Problems/Problem 17"
Mrdavid445 (talk | contribs) (Created page with "==Problem== Pauline Bunyan can shovel snow at the rate of <math>20</math> cubic yards for the first hour, <math>19</math> cubic yards for the second, <math>18</math> for the thi...") |
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<math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 12</math> | <math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 12</math> | ||
| + | |||
| + | ==Solution== | ||
| + | Her driveway has <math>(4)(10)(3)=120</math> cubic yards of snow. After the first hour she would have <math>120-20=100</math> cubic yards, then <math>100-19=81</math>, <math>81-18=63</math>, <math>63-17=46</math>, <math>46-16=30</math>, <math>30-15=15</math>, and <math>15-14=1</math> cubic yard after the seventh hour. It will take her a little more than seven hours to shovel it clean, which is closest to <math>\boxed{\text{(D)}\ 7}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1994|num-b=16|num-a=18}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:13, 4 July 2013
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
Solution
Her driveway has 
cubic yards of snow. After the first hour she would have 
cubic yards, then 
, 
, 
, 
, 
, and 
cubic yard after the seventh hour. It will take her a little more than seven hours to shovel it clean, which is closest to 
.
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
