1994 AMC 8 第 18 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
18.
Mike 离家后，先在城市交通中缓慢向东行驶。到达高速公路后，他更快地继续向东行驶，直到到达购物中心并停车。他在购物中心购物一小时。Mike 沿原路回家，先在高速公路上快速向西行驶，然后在城市交通中缓慢行驶。每个图的纵轴表示离家的距离，横轴表示离家后经过的时间。哪个图最能表示 Mike 的行程？
Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike’s trip?
小提示：
外出时离家的距离增加，购物一小时期间保持不变，回家时距离减少
Distance from home increases on the way out, stays constant during the hour of shopping, and decreases on the way back.
大提示：
城市慢速行驶对应较平缓的斜率，高速快速行驶对应较陡的斜率；在购物中心停车是一段水平线
Slow city driving is a gentle (shallow) slope and fast highway driving is a steep slope; the stop at the mall is a flat, horizontal segment.
解答：
去程中 Mike 先慢速行驶，对应平缓上升；再快速行驶，对应较陡上升。购物一小时期间离家距离不变，对应水平线段。
回程中他先快速行驶，对应较陡下降；再慢速行驶，对应较平缓下降。只有先慢后快上升、顶部水平、再先快后慢下降的图符合。
所以正确答案是 B。
On the way out Mike drives slowly (a shallow slope) then rapidly (a steep slope), so the distance rises slowly and then more steeply. During the hour at the mall the distance stays the same, a flat segment.
On the return he drives rapidly (steep) then slowly (shallow), so the distance falls steeply and then more gently. Only the graph with a slow-then-fast rise, a flat top, and a fast-then-slow fall fits.
Thus, the correct answer is B .
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