2023 AMC 8 Problems/Problem 15
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (Cheap)
- 5 Solution 4
- 6 Solution 5
- 7 Video Solution by Math-X (Let's first Understand the question)
- 8 Video Solution (CREATIVE THINKING!!!)
- 9 Animated Video Solution
- 10 Video Solution by Magic Square
- 11 Video Solution by Interstigation
- 12 Video Solution by harungurcan
- 13 See Also
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?
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)
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 .
To travel of a mile in total, each block must be of a mile long. Since Viswam takes minute to walk along each block, it would take him minutes normally.
Viswam has already travelled for mins by the time he encounters the detour, so he must travel block lengths in the remaining minutes. The distance he has to travel is of a mile. Therefore,
As mins equals hour, we set up the following proportion:
Cross multiplying and cancelling units yields
-Benedict T (countmath1)
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)
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by Magic Square
Video Solution by Interstigation
Video Solution by harungurcan
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