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Difference between revisions of "1994 AJHSME Problems/Problem 17"

(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>
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==Solution==
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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>.
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==See Also==
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{{AJHSME box|year=1994|num-b=16|num-a=18}}

Revision as of 00:04, 23 December 2012

Problem

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

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

Solution

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 $\boxed{\text{(D)}\ 7}$.

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
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