Question

Steve 和 LeRoy 在离岸 $1$ 英里的地方钓鱼时，船漏水了，水以每分钟 $10$ 加仑的恒定速度进入船内。若船中进水超过 $30$ 加仑，船就会沉。Steve 以每小时 $4$ 英里的恒定速度划向岸边，同时 LeRoy 把水舀出船。为了在船不沉的情况下到岸，LeRoy 最慢需要以每分钟多少加仑的速度舀水？

While Steve and LeRoy are fishing $1$ mile from shore, their boat springs a leak, and water comes in at a constant rate of $10$ gallons per minute. The boat will sink if it takes in more than $30$ gallons of water. Steve starts rowing toward the shore at a constant rate of $4$ miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?

$2$

$4$

$6$

$8$

$10$

答案：D

知识点：速率单位换算

难度评级：1310

解答：

以每小时 $4$ 英里划 $1$ 英里，需要 $\tfrac{1}{4}$ 小时，即 $15$ 分钟。这段时间进入 $15 \cdot 10 = 150$ 加仑水。

船内最多剩 $30$ 加仑，所以 LeRoy 必须舀出 $150 - 30 = 120$ 加仑，用时 $15$ 分钟，速率为加仑每分钟。 $\dfrac{120}{15} = 8$

所以正确答案是 D。

Rowing $1$ mile at $4$ miles per hour takes $\tfrac{1}{4}$ hour, or $15$ minutes. In that time $15 \cdot 10 = 150$ gallons of water enter the boat.

Since at most $30$ gallons may remain, LeRoy must bail $150 - 30 = 120$ gallons in $15$ minutes, a rate of $\dfrac{120}{15} = 8$ gallons per minute.

Thus, D is the correct answer.

2008 AMC 12A 第 7 题

答案：D

难度评级：1310

解答：

其他年份的第 7 题