Difference between revisions of "2023 AMC 8 Problems/Problem 15"
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| − | A | + | <math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 4.2 \qquad \textbf{(C)}\ 4.5 \qquad \textbf{(D)}\ 4.8 \qquad \textbf{(E)}\ 5</math> |
==Solution== | ==Solution== | ||
Revision as of 00:59, 25 January 2023
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?
![[asy] // Diagram by TheMathGuyd size(8cm); // this is an important stickman to the left of the origin pair C=midpoint((-0.5,0.5)--(-0.6,0.05)); draw((-0.5,0.5)--(-0.6,0.05)); // Head to butt draw((-0.64,0.16)--(-0.7,0.2)--C--(-0.47,0.2)--(-0.4,0.22)); // LH-C-RH draw((-0.6,0.05)--(-0.55,-0.1)--(-0.57,-0.25)); draw((-0.6,0.05)--(-0.68,-0.12)--(-0.8,-0.20)); filldraw(circle((-0.5,0.5),0.1),white,black); int i; real d,s; // gap and side d=0.2; s=1-2*d; for(i=0; i<10; i=i+1) { //dot((i,0), red); //marks to start filldraw((i+d,d)--(i+1-d,d)--(i+1-d,1-d)--(i+d,1-d)--cycle, lightgrey, black); filldraw(conj((i+d,d))--conj((i+1-d,d))--conj((i+1-d,1-d))--conj((i+d,1-d))--cycle,lightgrey,black); } 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),black); label("School", (10,0),E, Draw()); [/asy]](http://latex.artofproblemsolving.com/2/a/a/2aa8bca6a47b5fa16df243f0db179e92accd9898.png)
Solution
Note that Viswam walks at a constant speed 60 blocks per hour, as he takes 1 minute to walk each block. After walking 5 blocks, he has taken 5 minutes, and he has 5 minutes remaining, to walk 7 blocks. Therefore, he must walk at a speed of 7 * 60/5 = 84 blocks per hour to get to school on time, from the time he starts his detour. Since he normally walks 1/2 mile, which is equal to 10 blocks, 1 mile is equal to 20 blocks. Therefore, he must walk at 84/20 = 4.2 mph from the time he starts his detour, to get to school on time, so the answer is B.
(pianoboy)
Animated Video Solution
~Star League (https://starleague.us)
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. 
