AMC 8 2005 Problem 10
AMC8 2005 年第 10 题
行程问题★★☆☆☆
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?
Joe 从家步行去学校，当他意识到自己已经迟到时，已经走了总路程的一半，他跑完了剩下的路程，跑步的速度是步行速度的 3 倍。已知 Joe 步行的一半路程耗时 6 分钟，那么他从家到学校总共花了多少分钟？
- A.7
- B.7.3
- C.7.7
- D.8
- E.8.3
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
We can use the equation d=rt where is the distance, is the rate, and is the time. The distances he ran and walked are equal, so , where is the rate at which he ran, is the time for which he ran, is the rate at which he walked, and is the time for which he walked. Because he runs three times faster than he walks, . We want to find the time he ran, minutes. He traveled for a total of 6+2=8 minutes.
We know that it took Joe 6 minutes to walk halfway. If he ran 3 times as fast as that, he went minutes for the other half (as and if we multiply by 3 we are essentially dividing by 3 ). Therefore, we have 6 + 2 = 8 minutes.
According to d = rt, and if we assume the distance from home to school is 1 mile, then , meaning . Then, given that he runs 3 times the speed he walks, he runs at or . Also, note that he only has mile left to reach school. Therefore, once again using d = rt, , and t = 2. Combining the given 6 minutes and the deduced 2 minutes, we reach . -N.
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