AMC12 2025 A

AMC12 2025 A · Q1

AMC12 2025 A · Q1. It mainly tests Rates (speed), Coordinate geometry.

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?

安迪和贝齐都住在数学城。安迪在1:30骑自行车离开数学城，向正北方向以稳定的8英里/小时速度行驶。贝齐在2:30从同一地点骑自行车出发，向正东方向以稳定的12英里/小时速度行驶。他们何时距离共同起点恰好相等？

(A) 3{:}30 3{:}30

(B) 3{:}45 3{:}45

(D) 4{:}15 4{:}15

(E) 4{:}30 4{:}30

Answer

Correct choice: (E)

正确答案：（E）

Solution

At $2{:}30$, Andy is $8$ miles ahead. For every hour that they both travel, Betsy gains $4$ miles on Andy. Therefore, it will take her $2$ more hours to be the same distance from the starting point as Andy, which occurs at $\boxed{\textbf{(E) } 4{:}30}$.

在2:30时，安迪已经领先8英里。每小时贝齐比安迪多行进4英里。因此，她需要2小时才能与安迪距离起点相同，这发生在 $\boxed{\textbf{(E) } 4{:}30}$。

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