Question

Earl E. Bird 先生每天早上正好八点离家上班。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？

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、速度与时间一次方程

难度评级：1410

解答：

设准时所需时间为 $t$ 小时。题中的 $3$ 分钟等于 $0.05$ 小时，所以 $40(t+0.05)=60(t-0.05)$ 。化简得 $40t+2=60t-3$ ，从而 $t=0.25$ 。

路程为 $40(0.30)=12$ 英里，因此准时速度为 $\dfrac{12}{0.25}=48$ 英里每小时。

所以正确答案是 B。

Let $t$ hours be the on-time travel time. Since $3$ minutes is $0.05$ hours, $40(t+0.05)=60(t-0.05).$ Then $40t+2=60t-3,$ so $t=0.25.$

The distance is $40(0.30)=12$ miles, so the required speed is $\dfrac{12}{0.25}=48$ mph.

Thus, the correct answer is B.

2002 AMC 10A 第 12 题

答案：B

难度评级：1410

解答：

其他年份的第 12 题