AMC 8 2023 Problem 15
AMC8 2023 年第 15 题
行程问题★★★☆☆
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 每天要步行半英里去上学，他上学的路线由 10 个等长的街区组成，每走 1 个街区需要一分钟。今天，在走了 5 个街区后，Viswam 发现他必须绕路：要走 3 个等长的街区而不是 1 个街区才能到达下一个交叉路口。从他绕行开始，Viswam 必须以每小时多少英里的速度步行，才能像平常一样准时到校？
- A.4
- B.4.2
- C.4.5
- D.4.8
- E.5
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
Note that Viswam walks at a constant speed of 60 blocks per hour as he takes 1 minute to walk each block. After walking 5 blocks, he has taken 5 minutes and has 5 minutes remaining to walk 7 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 10 blocks, 1 mile is equal to 20 blocks. Therefore, he must walk at mph from the time he starts his detour to get to school on time, so the answer is 4.2.
Viswam walks 10 blocks, or half a mile, in 10 minutes. Therefore, he walks at a rate of 3 mph. When he takes his detour, he must travel 7 blocks instead of 5. Our final equation is .
When calculating the speed of his normal route, we get: Keep in mind that his route is 10 blocks long. Since we count 7 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 6 to get the rate, we get, . Therefore, the answer is 4.2.
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