The place I went to was very well equipped and it had a mangler to press the excess water from the rugs.
I returned later to get the rugs. They were not even nearly dry, but they did not drip any water anymore, so I could put them to the car more easily. At home I hung them on the pergola pilars. And the rugs are still there drying, it seems to take a while. Hope they are dry by tomorrow.