Page Two: the last run
Nudge. The river section and the road section are not the same length and they are not at the same end. Find where the track leaves the water.
Harder
The line runs over the Wupper from the eastern terminus as far as Sonnborner Strasse, and over the valley road for the last stretch after that. The road stretch is at the western end, so he was riding west.
The answer
The word is vohwinkel.
The Schwebebahn is above the river Wupper for about ten of its thirteen kilometres, and above the valley road for the remaining three and a bit, and the road section is the western end of the line. The clerk's docket says the run finished over the road, so he was travelling west, and the western terminus is Vohwinkel. The eastern one is Oberbarmen, which is where the river is still beneath you, and which is why it is the wrong answer.