1973 AMC 12 第 34 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。
34.
一架飞机逆风直飞两座城镇之间，耗时 分钟；顺风返回所需时间比无风时少 分钟。返程所需的分钟数（有两个答案）为
A plane flew straight against a wind between two towns in minutes and returned with that wind in minutes less than it would take in still air. The number of minutes (two answers) for the return trip was
或
or
或
or
或
or
或
or
或
or
小提示：
设返程时间为 ；则无风时的飞行时间为
Let be the return time; the still-air time is then
大提示：
飞机在无风时的速度是逆风与顺风地速的平均值
The plane’s still-air speed is the average of its against-wind and with-wind ground speeds
解答：
设两城距离为 ，返程时间为 分钟。逆风与顺风速度分别为 与 。它们的平均值是无风速度 。因此 清除分母，得到 两个正值都符合题设条件，所以两个返程时间为 分钟与 分钟。
所以正确答案是 C。
Let the distance be and the return time be minutes. The against-wind and with-wind speeds are and Their average is the still-air speed Therefore Clearing denominators gives Both positive values are consistent with the stated conditions, so the two return times are and minutes.
Therefore, the correct answer is C.