A cyclist, coasting on level ground, comes to a junction (Point A in the figure) where he can either continue to coast on level ground to Point B (Path I)

or take a path down and back up to Point B (Path II). The cyclist coasts along either path: drag and friction are negligible. Which path is fastest (I or II) or do they take equal time? Why? (This problem was inspired by just this situation, which I encountered while riding across campus at UC Irvine about 35 years ago.)

Fig: 1

Fig: 2