Question

Steve 和 LeRoy 在离岸 $1$ 英里处钓鱼时，船开始漏水，水以每分钟 $10$ 加仑的恒定速度进入。若进水超过 $30$ 加仑，船就会沉。Steve 开始以每小时 $4$ 英里的恒定速度向岸边划船，同时 LeRoy 往外舀水。若他们要在不沉船的情况下到达岸边，LeRoy 最慢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：1280

解答：

以每小时 $4$ 英里的速度，Steve 划 $1$ 英里需要 $15$ 分钟。这段时间会有 $15 \cdot 10 = 150$ 加仑水进入。

为了不超过 $30$ 加仑，LeRoy 必须在 $15$ 分钟内舀出 $150 - 30 = 120$ 加仑，即每分钟 $\dfrac{120}{15} = 8$ 加仑。

所以正确答案是 D。

At $4$ miles per hour, Steve rows $1$ mile in $15$ minutes. During that time $15 \cdot 10 = 150$ gallons enter.

To stay under $30$ gallons, LeRoy must bail $150 - 30 = 120$ gallons in $15$ minutes, or $\dfrac{120}{15} = 8$ gallons per minute.

Thus, the correct answer is D.

2008 AMC 10A 第 11 题

答案：D

难度评级：1280

解答：

其他年份的第 11 题