Question

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

Solution:

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 Problem 1

Solution:

Problem 1 in Other Years