2023 AMC 8 Problems/Problem 15
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[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 of 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, apex304 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 3 (Cheap)
Notice that Viswam will need to walk blocks during the second half as opposed to his normal blocks. Since rate is equal to distance over time, this implies that the final answer will likely be a multiple of , since you will need to convert blocks to miles. The only answer choice that is a multiple of is .
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/1bA7fD7Lg54?t=1221
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 |
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