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Neue Kasseler Straße
Close to the central train station is an on-ramp to the B3. It is located at the traffic lights where Neue Kasseler Straße and Zimmermannstraße intersect. About 5 min. walk from the train station. If you are planing to get to the Autobahn (see below) almost anyone can take you as far as to where the B3 meets the B62. There is a roundabout where you can be dropped and from there you should get to Alsfeld quite fast.
ESSO petrol station
There is an ESSO petrol station right in Marburg underneath Kurt-Schumacher-Brücke on B3 Schnellstraße in northern direction. From there it should be possible to reach Kassel on B3 or the B62 to Alsfeld though it can take some hour or two as there are only few cars refuelling at this place. You reach the station within five minutes walking from the city center of Marburg.
You also might consider going north via Gießen. It´s a little detour, but you reach the Autobahn A5 faster (it´s ~ 30 km to Gießen, but ~ 90 km to Kassel).
Northward on x27px/ Kassel, Göttingen, Hannover, Hamburg and Southward on x27px/ Frankfurt, Darmstadt, Basel
Rasthof und Hotel Pfefferhöhe
A good place to travel in northern or southern direction on A5/E 40 is Rasthof Pfefferhöhe near Alsfeld on 'Grünberger Straße'. If you have a 'Semesterticket' of the University of Marburg, you might want to consider taking the train or bus to Alsfeld, although it should be possible to get to Alsfeld hitchhiking along the B62 within one hour. According to googlemaps there is a McD's restaurant at this place as well.
Araltankstelle - Aral-Petrol station
An easy way to hitchhike out of Marburg in southern direction is the Aral - Petrol station near Südbahnhof (the train station in Frauenbergstraße). To go there, you can either walk, or take a bus from Rudolphsplatz (e.g. 1, 4, 6, (7), ...). Get out of the bus at "Südbahnhof". There´s a footbridge to the other side of the rails and B3. The street name is "Am Krekel". Walk toward south, out of the town. After about 3 minutes, you can see the blue sign of a petrol station (Aral) on you left. There are several fences and smaller paths leading to parkings and one (I think it´s painted in white) leading to the petrol station. It might take some minutes as there is not too much traffic, but you´ll find someone to pick you up...
This spot is good for southern directions as Gießen, Frankfurt,... you can also try to go to Gießen this way and change directions towards north. That might be a little tricky though.
Coming from East and North
Get to the on-ramp 2 "Alsfeld Ost" on the A5. From there best continue with a sign "Marburg". Easy to get a ride from here especially in the afternoon.
Coming from South
Try the petrol station "Wetterau" on the A5 and directly ask for Marburg. Might be lucky. If not take the detour to Alsfeld.