The time required for each ball to traverse its path is the horizontal displacement divided by the average horizontal velocity. The High and Low Road paths have equal horizontal displacements, but the Low Road has the greater average horizontal velocity. Thus, the Low Road takes the lesser time. Why? Because the normal force of the Low Road track produces an instantaneous horizontal velocity that is always equal to or greater than the instantaneous horizontal velocity produced by the normal force of the High Road track. (Note that the other two forces on the ball, gravity and static friction, do not enter this argument. Why not?) This outcome holds true for any lower path shape as long as the ball does not slip or leave the track. Demo PDF Less