AMC8 2023

AMC8 2023 · Q15

AMC8 2023 · Q15. It mainly tests Unit conversion, Rates (speed).

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? Here’s a hint: if you aren’t correct, think about using conversions, maybe that’s why you’re wrong! -RyanZ4552

Viswam每天走半英里上学。他的路线包括10个等长城市街区，每块街区走1分钟。今天，走5个街区后，Viswam发现必须绕道，走3个等长街区代替1个街区到达下一个拐角。从开始绕道时起，他必须以多少mph的速度走，才能按平常时间到校？提示：如果不对，想想单位换算，也许那是错的原因！-RyanZ4552

(A) \ 4 \ 4

(B) \ 4.2 \ 4.2

(D) \ 4.8 \ 4.8

(E) \ 5 \ 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

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 $7 \cdot 60 \div 5 = 84$ blocks per hour to get to school on time, from the time he starts his detour. Since he normally walks $\frac{1}{2}$ mile, which is equal to $10$ blocks, $1$ mile is equal to $20$ blocks. Therefore, he must walk at $84 \div 20 = 4.2$ mph from the time he starts his detour to get to school on time, so the answer is $\boxed{\textbf{(B)}\ 4.2}$.

注意Viswam正常速度为60街区/小时，因为每街区1分钟。走5街区用5分钟，还剩5分钟走剩余距离。但因绕道，原剩5街区，现需走3+4=7街区（绕道3代替1，原路线剩5，现多2，总7）。因此，从绕道开始，他须以$7 \cdot 60 \div 5 = 84$街区/小时走。正常半英里=10街区，故1英里=20街区。因此速度$84 \div 20 = 4.2$ mph。\boxed{\textbf{(B)}\ 4.2}

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