AMC12 2008 A

AMC12 2008 A · Q7

AMC12 2008 A · Q7. It mainly tests Rates (speed), Work problems.

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 towards 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?

当 Steve 和 LeRoy 在离岸 1 英里处钓鱼时，他们的船突然漏水，水以每分钟 10 加仑的恒定速率流入。若进水超过 30 加仑，船将下沉。Steve 以每小时 4 英里的恒定速度开始向岸边划船，同时 LeRoy 往外舀水。为了在不沉没的情况下到达岸边，LeRoy 舀水的最慢速率（加仑/分钟）是多少？

(A) 2 2

(B) 4 4

(D) 8 8

(E) 10 10

Answer

Correct choice: (D)

正确答案：（D）

Solution

It will take $\frac{1}{4}$ of an hour or $15$ minutes to get to shore. Since only $30$ gallons of water can enter the boat, only $\frac{30}{15}=2$ net gallons can enter the boat per minute. Since $10$ gallons of water enter the boat each minute, LeRoy must bail $10-2=8$ gallons per minute $\Rightarrow\mathrm{(D)}$.

到岸边需要 $\frac{1}{4}$ 小时，即 $15$ 分钟。由于船内最多只能进 $30$ 加仑水，所以每分钟净进水量最多为 $\frac{30}{15}=2$ 加仑。每分钟有 $10$ 加仑水进入船内，因此 LeRoy 必须每分钟舀出 $10-2=8$ 加仑 $\Rightarrow\mathrm{(D)}$。

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