2003 Cayley Problem 21

Troye and Daniella are running at constant speeds in opposite directions around a circular track. Troye completes one lap every 56 seconds and meets Daniella every 24 seconds. How many seconds does it take Daniella to complete one lap?

\textbf{(A)}\ 32\quad \textbf{(B)}\ 36\quad \textbf{(C)}\ 40\quad \textbf{(D)}\ 48\quad \textbf{(E)}\ 42

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.