2023 AMC 8 Problems/Problem 15
Contents
[hide]- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3
- 5 Video Solution by Math-X (Let's first Understand the question)
- 6 Video Solution by CoolMathProblems
- 7 Video Solution (CREATIVE THINKING!!!)
- 8 Animated Video Solution
- 9 Video Solution by Magic Square
- 10 Video Solution by Interstigation
- 11 Video Solution by harungurcan
- 12 Video Solution (Solve under 60 seconds!!!)
- 13 Video Solution by Dr. David
- 14 Video Solution by WhyMath
- 15 See Also
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 of blocks per hour as he takes
minute to walk each block. After walking
blocks, he has taken
minutes and 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, apex304 and MrThinker)
Solution 2
Viswam walks blocks, or half a mile, in
minutes. Therefore, he walks at a rate of
mph. When he takes his detour, he must travel
blocks instead of
. Our final equation is
.
Note: In the second half of his journey, he is travelling 7/5 as far as he originally expected to, so he needs to travel at 7/5 the speed to get there on time.
Solution 3
When calculating the speed of his normal route, we get:
Keep in mind that his route is blocks long. Since we count
blocks when the detour starts, than this would mean that he has
miles left to walk, considering the normal amount of blocks that he usually walks. Multiplying by
to get the rate, we get,
Therefore, the answer is .
Video Solution by Math-X (Let's first Understand the question)
https://youtu.be/Ku_c1YHnLt0?si=sWlX8leEM3rALWLK&t=2686
~Math-X
Video Solution by CoolMathProblems
https://youtu.be/9WP3LQaMIVg?feature=shared&t=510
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4153
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=1626
Video Solution by harungurcan
https://www.youtube.com/watch?v=otNV1MviJsA&t=20s
~harungurcan
Video Solution (Solve under 60 seconds!!!)
https://youtu.be/6O5UXi-Jwv4?si=KvvABit-3-ZtX7Qa&t=681
~hsnacademy
Video Solution by Dr. David
Video Solution by WhyMath
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.