2014 Fermat Problem 22

Jillian drives along a straight road that goes directly from her house (J) to her Grandfather's house (G). Some of this road is on flat ground and some is downhill or uphill. Her car travels downhill at 99 km/h, on flat ground at 77 km/h, and uphill at 63 km/h. It takes Jillian 3 hours and 40 minutes to drive from J to G. It takes her 4 hours and 20 minutes to drive from G to J. The distance between J and G, in km, is

\textbf{(A)}\ 318\tfrac{2}{3}\quad \textbf{(B)}\ 324\quad \textbf{(C)}\ 308\quad \textbf{(D)}\ 292\tfrac{3}{5}\quad \textbf{(E)}\ 292\tfrac{1}{9}

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