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 number of hours since $1{:}30.$ Andy has traveled $8t$ miles north, and Betsy, who started an hour later, has traveled $12(t-1)$ miles east.

Setting the distances equal, $8t = 12(t-1),$ so $4t = 12$ and $t = 3.$

Three hours after $1{:}30$ is $4{:}30.$

Thus, the correct answer is E.

2025 AMC 12A Problem 1

Solution:

Problem 1 in Other Years