2025 Cayley Problem 20

In the diagram, line segment CD has length 48 cm. Two ants, Violet and Petunia, are at point C and plan to walk to point D. Violet walks along four congruent semi-circles above CD. Petunia walks along three congruent semi-circles below CD.

Violet and Petunia start walking at the same time, and they walk at constant, but different, speeds. Petunia arrives at D 12 seconds before Violet and travels 3 times as quickly as Violet. How long does it take Violet to walk from C to D?

\textbf{(A)}\ 24\ \text{seconds}\quad \textbf{(B)}\ 18\ \text{seconds}\quad \textbf{(C)}\ 36\ \text{seconds}\quad \textbf{(D)}\ 16\ \text{seconds}\quad \textbf{(E)}\ 21\ \text{seconds}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.