Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2017 AMC 10A Problems/Problem 7"

m
m (→‎Solution)
 
(One intermediate revision by one other user not shown)
Line 5: Line 5:
 
==Solution==
 
==Solution==
  
−
Let <math>j</math> represent how far Jerry walked, and <math>s</math> represent how far Sylvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides,  
+
Let <math>j</math> represent how far Jerry walked, and <math>s</math> represent how far Silvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides,  
 
<math>j = 2</math>
 
<math>j = 2</math>
 
Since Silvia walked the diagonal, she walked the hypotenuse of a <math>45</math>, <math>45</math>, <math>90</math> triangle with leg length <math>1</math>. Thus,
 
Since Silvia walked the diagonal, she walked the hypotenuse of a <math>45</math>, <math>45</math>, <math>90</math> triangle with leg length <math>1</math>. Thus,
Line 14: Line 14:
 
==Video Solution==
 
==Video Solution==
 
https://youtu.be/pxg7CroAt20
 
https://youtu.be/pxg7CroAt20
 +
 +
https://youtu.be/MUxbCp-2OYQ
 +
 +
~savannahsolver
  
 
==See Also==
 
==See Also==

Latest revision as of 21:40, 1 November 2023

Problem

Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia's trip was, compared to Jerry's trip?

$\textbf{(A)}\ 30\%\qquad\textbf{(B)}\ 40\%\qquad\textbf{(C)}\ 50\%\qquad\textbf{(D)}\ 60\%\qquad\textbf{(E)}\ 70\%$

Solution

Let $j$ represent how far Jerry walked, and $s$ represent how far Silvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides, $j = 2$ Since Silvia walked the diagonal, she walked the hypotenuse of a $45$, $45$, $90$ triangle with leg length $1$. Thus, $s = \sqrt{2} = 1.414...$ We can then take $\frac{j-s}{j} \approx \frac{2 - 1.4}{2}=0.3 \implies \boxed{\textbf{(A)}\ 30\%}$

Video Solution

https://youtu.be/pxg7CroAt20

https://youtu.be/MUxbCp-2OYQ

~savannahsolver

See Also

2017 AMC 10A (Problems • Answer Key • Resources)
Preceded by
Problem 6 		Followed by
Problem 8
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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10A_Problems/Problem_7&oldid=200608"