2011 AMC 12A 第 12 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。
12.
一艘机动船和一只木筏都从河上的码头 出发，向下游前进。木筏以河水水流速度漂流。机动船相对于河水保持恒定速度。机动船到达下游码头 后，立即掉头向上游返回。离开码头 小时后，它在河上与木筏相遇。机动船从 到 花了多少小时？
A power boat and a raft both left dock on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river hours after leaving dock How many hours did it take the power boat to go from to
小提示：
在水流参考系中思考，此时木筏静止不动
Work in the frame of the water, in which the raft stays put
大提示：
相对于河水，船往返速度相同，所以去程和回程用时相等
Relative to the water the boat travels at the same speed going out and coming back, so it takes equal times each way
解答：
全部相对于河水来测量。在这个参考系中，木筏静止在船出发的位置，而船相对于河水以恒定速度 运动，下游和上游方向都是如此。
船离开木筏，向外行驶一段时间，再以相同的相对速度返回木筏，所以去程和回程用时相等。因此到 的下行路程花了 的一半，即 小时。
因此，正确答案是 D。
Measure everything relative to the water. In that frame the raft is stationary at the point where the boat started, and the boat moves at its constant speed relative to the water, both downstream and upstream.
The boat leaves the raft, travels away for some time, then returns to it at the same relative speed, so it spends equal times going and returning. Hence the outbound leg to takes half of which is hours.
Thus, the correct answer is D.
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