2017 Cayley Problem 20

Car X and Car Y are travelling in the same direction in two different lanes on a long straight highway. Car X is travelling at a constant speed of 90 km/h and has a length of 5 m. Car Y is travelling at a constant speed of 91 km/h and has a length of 6 m. Car Y starts behind Car X and eventually passes Car X. The length of time between the instant when the front of Car Y is lined up with the back of Car X and the instant when the back of Car Y is lined up with the front of Car X is t seconds. The value of t is

\textbf{(A)}\ 39.6\quad \textbf{(B)}\ 18.0\quad \textbf{(C)}\ 21.6\quad \textbf{(D)}\ 46.8\quad \textbf{(E)}\ 32.4

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.