Question

Andy 和 Betsy 都住在 Mathville。Andy 在一点半从 Mathville 骑自行车出发，以稳定的每小时 $8$ 英里正北行驶。Betsy 在两点半从同一点骑自行车出发，以稳定的每小时 $12$ 英里正东行驶。什么时候他们离共同出发点的距离恰好相同？

Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at 1:30, traveling due north at a steady $8$ miles per hour. Betsy leaves on her bicycle from the same point at 2:30, traveling due east at a steady $12$ miles per hour. At what time will they be exactly the same distance from their common starting point?

3:30

3:45

4:00

4:15

4:30

答案：E

知识点：路程、速度与时间一次方程

难度评级：860

解答：

设 $t$ 为从一点半起经过的小时数。Andy 向北走了 $8t$ 英里。Betsy 晚一小时出发，所以她向东走了 $12(t-1)$ 英里。要求两人的距离相等，即 $8t = 12(t-1)$ 。因此 $4t = 12$ ， $t = 3$ 。一点半之后三小时是四点半。因此正确答案是 E。

Let $t$ be the hours since 1:30. Andy has gone $8t$ miles north. Betsy starts an hour later, so she's gone $12(t-1)$ miles east. We want these equal: $8t = 12(t-1).$ That gives $4t = 12,$ so $t = 3.$ Three hours past 1:30 is 4:30. Thus, E is the correct answer.

2025 AMC 10A 第 1 题

答案：E

难度评级：860

解答：

其他年份的第 1 题