Question

Earl E. Bird 先生每天上午八点整离家上班。当他的平均速度为每小时 $40$ 英里时，会晚到三分钟；当平均速度为每小时 $60$ 英里时，会早到三分钟。Bird 先生应以多少英里每小时的平均速度行驶，才能准时到达工作地点？

Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages $40$ miles per hour, he arrives at his workplace three minutes late. When he averages $60$ miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?

$45$

$48$

$50$

$55$

$58$

答案：B

知识点：路程、速度与时间方程组

难度评级：1380

解答：

设准时所需时间为 $t$ 小时。三分钟是 $0.05$ 小时，所以 $40(t+0.05) = 60(t-0.05)$ 。

得 $40t + 2 = 60t - 3$ ，所以 $t = 0.25$ 。路程为 $40(0.25+0.05) = 12$ 英里，所需速度为 $\dfrac{12}{0.25} = 48$ 英里每小时。

因此，正确答案是 B。

Let $t$ be the time in hours to arrive on time. Since three minutes is $0.05$ hours, $40(t+0.05) = 60(t-0.05).$

This gives $40t + 2 = 60t - 3,$ so $t = 0.25.$ The distance is $40(0.25+0.05) = 12$ miles, and the required speed is $\dfrac{12}{0.25} = 48$ miles per hour.

Thus, the correct answer is B.

2002 AMC 12A 第 11 题

答案：B

难度评级：1380

解答：

其他年份的第 11 题