Difference between revisions of "2023 AMC 8 Problems/Problem 15"
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==Problem== | ==Problem== | ||
− | Viswam walks half a mile to get to school each day. His route consists of 10 city blocks of equal length and he takes 1 minute to walk each block. Today, after walking 5 blocks, Viswam discovers he has to make a detour, walking 3 blocks of equal length instead of 1 block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk, in order to get to school at his usual time? | + | Viswam walks half a mile to get to school each day. His route consists of <math>10</math> city blocks of equal length and he takes <math>1</math> minute to walk each block. Today, after walking <math>5</math> blocks, Viswam discovers he has to make a detour, walking <math>3</math> blocks of equal length instead of <math>1</math> block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk, in order to get to school at his usual time? |
− | |||
<asy> | <asy> | ||
// Diagram by TheMathGuyd | // Diagram by TheMathGuyd | ||
− | size( | + | size(10cm); |
// this is an important stickman to the left of the origin | // this is an important stickman to the left of the origin | ||
pair C=midpoint((-0.5,0.5)--(-0.6,0.05)); | pair C=midpoint((-0.5,0.5)--(-0.6,0.05)); | ||
Line 26: | Line 25: | ||
fill((5+d,-d/2)--(6-d,-d/2)--(6-d,d/2)--(5+d,d/2)--cycle,lightred); | fill((5+d,-d/2)--(6-d,-d/2)--(6-d,d/2)--(5+d,d/2)--cycle,lightred); | ||
− | draw((0,0)--(5,0)--(5,1)--(6,1)--(6,0)--(10.1,0),deepblue); | + | draw((0,0)--(5,0)--(5,1)--(6,1)--(6,0)--(10.1,0),deepblue); //Who even noticed |
label("School", (10,0),E, Draw()); | label("School", (10,0),E, Draw()); | ||
</asy> | </asy> | ||
− | |||
<math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 4.2 \qquad \textbf{(C)}\ 4.5 \qquad \textbf{(D)}\ 4.8 \qquad \textbf{(E)}\ 5</math> | <math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 4.2 \qquad \textbf{(C)}\ 4.5 \qquad \textbf{(D)}\ 4.8 \qquad \textbf{(E)}\ 5</math> | ||
Revision as of 01:25, 26 January 2023
Contents
[hide]Problem
Viswam walks half a mile to get to school each day. His route consists of city blocks of equal length and he takes
minute to walk each block. Today, after walking
blocks, Viswam discovers he has to make a detour, walking
blocks of equal length instead of
block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk, in order to get to school at his usual time?
Solution 1
Note that Viswam walks at a constant speed blocks per hour, as he takes
minute to walk each block. After walking
blocks, he has taken
minutes, and he has
minutes remaining, to walk
blocks. Therefore, he must walk at a speed of
blocks per hour to get to school on time, from the time he starts his detour. Since he normally walks
mile, which is equal to
blocks,
mile is equal to
blocks. Therefore, he must walk at
mph from the time he starts his detour, to get to school on time, so the answer is
.
pianoboy (Edits by ILoveMath31415926535 and MrThinker)
Solution 2
Viswam walks blocks, or half a mile, in
minutes. Therefore, he walks at a rate of
mph. From the time he takes his detour, he must travel
blocks instead of
. Our final equation is
Solution by ILoveMath31415926535
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4153
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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.