2025 AMC 10A Problem 1

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?

\textbf{(A)} 3{:}30 \qquad \textbf{(B)} 3{:}45 \qquad \textbf{(C)} 4{:}00 \qquad \textbf{(D)} 4{:}15 \qquad \textbf{(E)} 4{:}30

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.