Question

一艘机动船和一只木筏都从河上的码头 $A$ 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 $B$ 后，立即掉头向上游返回。离开码头 $A$ $9$ 小时后，它在河上与木筏相遇。机动船从 $A$ 到 $B$ 花了多少小时？

A power boat and a raft both left dock $A$ 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 $B$ downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river $9$ hours after leaving dock $A.$ How many hours did it take the power boat to go from $A$ to $B?$

$3$

$3.5$

$4$

$4.5$

$5$

答案：D

知识点：相对速度路程、速度与时间对称性

难度评级：1580

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 $v$ 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 $B$ 的下行路程花了 $9$ 的一半，即 $4.5$ 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 $v$ 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 $B$ takes half of $9,$ which is $4.5$ hours.

Thus, the correct answer is D.

2011 AMC 12A 第 12 题

答案：D

难度评级：1580

解答：

其他年份的第 12 题