Stateing Past Actions With Specified Time

Solution 1:

There is no rule concerning whether we state the start-time of an action, its end-time or its duration.

If the action takes as long as it does to wash a car we would probably say, "I washed the car this morning," or if more precision is needed, "At 11.00 this morning I went (out) and washed the car." If even greater precision is called for we might say, "I washed the car from 11.00 till 12.00 this morning." One would only need to tell one's wife, "I washed the car from 11.00 till 11.59 this morning" if she was profoundly suspicious.

You suggest: "I washed the car at exactly 11:59"(actions final point) We wouldn't say that, though we might say, "I finished washing the car at exactly 11.59."