AMC10 2008 A

AMC10 2008 A · Q11

AMC10 2008 A · Q11. 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 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?

当史蒂夫和勒罗伊在离岸1英里的地方钓鱼时，他们的船漏水了，水以每分钟10加仑的恒定速率进入船内。如果船内进水超过30加仑，船就会沉没。史蒂夫开始以每小时4英里的恒定速率向岸边划船，同时勒罗伊从船中舀水。他们到达岸边而不沉没，勒罗伊舀水的速率最慢是多少加仑每分钟？

(A) 2 2

(B) 4 4

(D) 8 8

(E) 10 10

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): At the rate of 4 miles per hour, Steve can row a mile in 15 minutes. During that time $15 \cdot 10 = 150$ gallons of water will enter the boat. LeRoy must bail $150 - 30 = 120$ gallons of water during that time. So he must bail at the rate of at least $\frac{120}{15} = 8$ gallons per minute.

答案（D）：以每小时 4 英里的速度，Steve 划 1 英里需要 15 分钟。在这段时间里，会有 $15 \cdot 10 = 150$ 加仑的水进入船中。LeRoy 必须在这段时间内舀出 $150 - 30 = 120$ 加仑的水。因此，他舀水的速度至少应为 $\frac{120}{15} = 8$ 加仑/分钟。

Topics