2021 Cayley Problem 18

Elina and Gustavo leave Cayley H.S. at 3:00 p.m. Elina runs north at a constant speed of 12 km/h. Gustavo walks east at a constant speed of 5 km/h. After 12 minutes, Elina and Gustavo change direction and travel directly towards each other, still at 12 km/h and 5 km/h, respectively. The time that they will meet again is closest to

\textbf{(A)}\ 3:24 p.m.\quad \textbf{(B)}\ 3:35 p.m.\quad \textbf{(C)}\ 3:25 p.m.\quad \textbf{(D)}\ 3:29 p.m.\quad \textbf{(E)}\ 3:21 p.m.

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.