Self-service bays are sold by time, not by car. You pay at a meter — coin, card or a token bought inside — and the clock starts.
A dial selects the function: pre-wash, wash, sometimes a foam brush, then rinse. When the timer runs out, it stops, whether or not you have finished the roof.
Prices are set per site and change, so the only reliable figures are the ones on the meter in front of you. What is predictable is the pattern of the cost: a small amount of money, a moderate amount of your time, and the whole job done by you.
Budget for two rounds if the car is properly dirty, and for getting wet in the process.
Attended arches and forecourt hand washes work differently — a fixed price per car, and someone else does the work while you wait.
** It is quick on mud, it is cheap per visit, and if you enjoy doing the car yourself it is the most direct route to a clean one.