Difference between revisions of "2003 AMC 10B Problems/Problem 5"
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Since the swath Moe actually mows is <math>24</math> inches, or <math>2</math> feet wide, he mows <math>10000</math> square feet in one hour. His lawn has an area of <math>13500</math>, so it will take Moe <math>1.35</math> hours to finish mowing the lawn. Thus the answer is <math>\boxed{\textbf{(C) } 1.35}</math>. | Since the swath Moe actually mows is <math>24</math> inches, or <math>2</math> feet wide, he mows <math>10000</math> square feet in one hour. His lawn has an area of <math>13500</math>, so it will take Moe <math>1.35</math> hours to finish mowing the lawn. Thus the answer is <math>\boxed{\textbf{(C) } 1.35}</math>. | ||
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| + | ==Solution 2== | ||
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| + | Let's assume that the swath moves back and forth; parallel to the 150 feet side. The length we cover in one strip of grass is <math>90</math> feet or <math>150</math> feet, but it doesn't matter, because in later calculations, we get the same result. Now we need to find out how many strips there are. In reality, the swath Moe mows is <math>24</math> inches wide, which can be easily translated into <math>2</math> feet. \frac{150}{2} is the number of strips Moe needs to mow, which is equal to <math>75</math>. We now compute | ||
==See Also== | ==See Also== | ||
Revision as of 19:28, 8 July 2020
- The following problem is from both the 2003 AMC 12B #4 and 2003 AMC 10B #5, so both problems redirect to this page.
Contents
Problem
Moe uses a mower to cut his rectangular 
-foot by 
-foot lawn. The swath he cuts is 
inches wide, but he overlaps each cut by 
inches to make sure that no grass is missed. He walks at the rate of 
feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow the lawn.
Solution
Since the swath Moe actually mows is 
inches, or 
feet wide, he mows 
square feet in one hour. His lawn has an area of 
, so it will take Moe 
hours to finish mowing the lawn. Thus the answer is 
.
Solution 2
Let's assume that the swath moves back and forth; parallel to the 150 feet side. The length we cover in one strip of grass is feet or feet, but it doesn't matter, because in later calculations, we get the same result. Now we need to find out how many strips there are. In reality, the swath Moe mows is inches wide, which can be easily translated into feet. \frac{150}{2} is the number of strips Moe needs to mow, which is equal to 
. We now compute
See Also
| 2003 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 AMC 12 Problems and Solutions | |
| 2003 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
