How do I add drainage to an existing garage floor?

When I park my car or truck in my garage water from rain or snow drips of the car and runs all over. Most garage floors are pitched toward the doors or a floor drain, mine does not have any pitch to it so the water ends up running into my workshop in the front of the garage and also runs into the walls where it is wicked up by the sheetrock. I am thinking about cutting 1/2" wide by 1/4" deep trenches in the floor around the cars to chanel the water to a drain basin. I don't want to use floor mats, and I don't want to install trench drains. Any ideas?