2005 Fermat Problem 19

Sam bicycles at 16 km/h and Chris bicycles at 24 km/h. At noon, Sam is 1 km north of Chris, and each begins to ride north. How many minutes will it take for Chris to catch Sam?

\textbf{(A)}\ 1\frac{1}{2}\quad \textbf{(B)}\ 2\frac{1}{2}\quad \textbf{(C)}\ 3\frac{3}{4}\quad \textbf{(D)}\ 7\frac{1}{2}\quad \textbf{(E)}\ 8

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