2011 Cayley Problem 24

Dolly, Molly and Polly each can walk at 6 km/h. Their one motorcycle, which travels at 90 km/h, can accommodate at most two of them at once (and cannot drive by itself!). Let t hours be the time taken for all three of them to reach a point 135 km away. Ignoring the time required to start, stop or change directions, what is true about the smallest possible value of t?

\textbf{(A)}\ t < 3.9\quad \textbf{(B)}\ 3.9 \le t < 4.1\quad \textbf{(C)}\ 4.1 \le t < 4.3\quad \textbf{(D)}\ 4.3 \le t < 4.5\quad \textbf{(E)}\ t \ge 4.5

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