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Difference between revisions of "2003 AMC 10B Problems/Problem 5"

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{{duplicate|[[2003 AMC 12B Problems|2003 AMC 12B #4]] and [[2003 AMC 10B Problems|2003 AMC 10B #5]]}}
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==Problem==
 
==Problem==
  
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Moe uses a mower to cut his rectangular <math>90</math>-foot by <math>150</math>-foot lawn. The swath he cuts is <math>28</math> inches wide, but he overlaps each cut by <math>4</math> inches to make sure that no grass is missed. He walks at the rate of <math>5000</math> 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.
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Moe uses a mower to cut his rectangular <math>90</math>-foot by <math>150</math>-foot lawn. The swath he cuts is <math>28</math> inches wide, but he overlaps each cut by <math>4</math> inches to make sure that no grass is missed. He walks at the rate of <math>5000</math> 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?
  
 
<math>\textbf{(A) } 0.75 \qquad\textbf{(B) } 0.8 \qquad\textbf{(C) } 1.35 \qquad\textbf{(D) } 1.5 \qquad\textbf{(E) } 3 </math>
 
<math>\textbf{(A) } 0.75 \qquad\textbf{(B) } 0.8 \qquad\textbf{(C) } 1.35 \qquad\textbf{(D) } 1.5 \qquad\textbf{(E) } 3 </math>
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==Solution==
 
==Solution==
  
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Since the swathe Moe actually mows is <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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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 (very easy to understand)==
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Let's assume that the swath moves back and forth; parallel to the <math>90</math> feet side. Thus, the length of one strip is <math>90</math> feet. 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. <math>\frac{150}{2}</math> is the number of strips Moe needs to mow, which is equal to <math>75</math>.
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Therefore, the total number of feet Moe mows is <math>75\times90</math>. Since Moe's mowing rate is <math>5000</math> feet per hour, <math>\frac{75\times90}{5000}</math> is the number of hours it takes him to do his job. Using basic calculations, we compute the answer. <math>\boxed{\textbf{(C) } 1.35}</math>.
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~sakshamsethi
  
 
==See Also==
 
==See Also==
  
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{{AMC12 box|year=2003|ab=B|num-b=3|num-a=5}}
 
{{AMC10 box|year=2003|ab=B|num-b=4|num-a=6}}
 
{{AMC10 box|year=2003|ab=B|num-b=4|num-a=6}}
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{{MAA Notice}}

Latest revision as of 16:23, 18 October 2023

The following problem is from both the 2003 AMC 12B #4 and 2003 AMC 10B #5, so both problems redirect to this page.

Problem

Moe uses a mower to cut his rectangular $90$-foot by $150$-foot lawn. The swath he cuts is $28$ inches wide, but he overlaps each cut by $4$ inches to make sure that no grass is missed. He walks at the rate of $5000$ 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?

$\textbf{(A) } 0.75 \qquad\textbf{(B) } 0.8 \qquad\textbf{(C) } 1.35 \qquad\textbf{(D) } 1.5 \qquad\textbf{(E) } 3$

Solution

Since the swath Moe actually mows is $24$ inches, or $2$ feet wide, he mows $10000$ square feet in one hour. His lawn has an area of $13500$, so it will take Moe $1.35$ hours to finish mowing the lawn. Thus the answer is $\boxed{\textbf{(C) } 1.35}$.


Solution 2 (very easy to understand)

Let's assume that the swath moves back and forth; parallel to the $90$ feet side. Thus, the length of one strip is $90$ feet. Now we need to find out how many strips there are. In reality, the swath Moe mows is $24$ inches wide, which can be easily translated into $2$ feet. $\frac{150}{2}$ is the number of strips Moe needs to mow, which is equal to $75$. Therefore, the total number of feet Moe mows is $75\times90$. Since Moe's mowing rate is $5000$ feet per hour, $\frac{75\times90}{5000}$ is the number of hours it takes him to do his job. Using basic calculations, we compute the answer. $\boxed{\textbf{(C) } 1.35}$.

~sakshamsethi

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

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