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 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 starting point?
$$\textbf{(A) } 3{:}30 \qquad\textbf{(B) } 3{:}45 \qquad\textbf{(C) } 4{:}00 \qquad\textbf{(D) } 4{:}15 \qquad\textbf{(E) } 4{:}30$$
Difficulty: 6/100 — Straightforward and easy to execute.
Core Concepts: $d=rt$
Challenges: Accounting for Betsy's 1-hour delay.
Techniques: Distance-rate-time setup.
Error-prone Steps: None.
Ideal Time:
Experienced: ≤ 20 sec
Intermediate: ≤ 40 sec
Beginner: ≤ 1-2 min