2014 Pascal Problem 24

Nadia walks along a straight path that goes directly from her house (N) to her Grandmother's house (G). Some of this path is on flat ground, and some is downhill or uphill. Nadia walks on flat ground at 5 km/h, walks uphill at 4 km/h, and walks downhill at 6 km/h. It takes Nadia 1 hour and 36 minutes to walk from N to G and 1 hour and 39 minutes to walk from G to N. If 2.5 km of the path between N and G is on flat ground, the total distance from N to G is closest to

\textbf{(A)}\ 8.0 \text{ km}\quad \textbf{(B)}\ 8.2 \text{ km}\quad \textbf{(C)}\ 8.1 \text{ km}\quad \textbf{(D)}\ 8.3 \text{ km}\quad \textbf{(E)}\ 7.9 \text{ km}

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 Pascal contests here.