Difference between revisions of "2023 AMC 8 Problems/Problem 13"
MRENTHUSIASM (talk | contribs) (Made the variable definition clearer, and reformatted the solution.) |
Themathguyd (talk | contribs) (Asy replaces png.) |
||
Line 5: | Line 5: | ||
finish lines. The <math>3</math>rd water station is located <math>2</math> miles after the <math>1</math>st repair station. How long is the race | finish lines. The <math>3</math>rd water station is located <math>2</math> miles after the <math>1</math>st repair station. How long is the race | ||
in miles? | in miles? | ||
− | + | ||
+ | <asy> | ||
+ | //Diagram By TheMathGuyd, The road is widened for bicycle safety | ||
+ | size(10cm); | ||
+ | real tl = 0.2; | ||
+ | real dpth = 0.8; | ||
+ | fill((0,0)--(8,0)--(8,1)--(0,1)--cycle,mediumgrey); | ||
+ | draw((0,.5)--(8,.5),dashed+white); | ||
+ | draw((0,0)--(8,0)--(8,1)--(0,1)--cycle,black); | ||
+ | draw((1,0)--(1,-tl)); | ||
+ | draw((2,0)--(2,-tl)); | ||
+ | draw((7,0)--(7,-tl)); | ||
+ | label(rotate(45)*"Water 1",(0.6,-dpth)); | ||
+ | label(rotate(45)*"Water 2",(1.6,-dpth)); | ||
+ | label(rotate(45)*"Water 7",(6.6,-dpth)); | ||
+ | label("\ldots\ldots",(4.2,-dpth)); | ||
+ | label(rotate(90)*"Start",(0,0.5),W); | ||
+ | label(rotate(-90)*"Finish",(8,0.5),E); | ||
+ | //Someone is going to see this and find out I don't know how to put borders on text and laugh. | ||
+ | real lh = 0.45; | ||
+ | real lr = 0.1; | ||
+ | path bx = (-lh,-lr)--(0,-lr)--(0,1+lr)--(-lh,1+lr)--cycle; | ||
+ | draw(bx); | ||
+ | draw(reflect((4,0),(4,1))*bx); | ||
+ | </asy> | ||
+ | |||
<math>\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 16 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 48 \qquad \textbf{(E)}\ 96</math> | <math>\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 16 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 48 \qquad \textbf{(E)}\ 96</math> | ||
Revision as of 11:55, 26 January 2023
Contents
[hide]Problem
Along the route of a bicycle race, water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also repair stations evenly spaced between the start and finish lines. The rd water station is located miles after the st repair station. How long is the race in miles?
Solution
Suppose that the race is miles long. The water stations are located at miles from the start, and the repair stations are located at miles from the start.
We are given that from which ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM
Video Solution (Animated)
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4439
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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.