Speed limits: continuous?

Driving in Florida, I remarked to my passenger that when I can see two speed limit signs ahead – say, 35 mph here, and 45 in the distance – I assume the speed limit is continuous: somewhere between the signs, the speed limit is 40.

My passenger disagreed. “The moment I see a speed sign in the distance, that’s the speed limit here and now. If I can see two signs, I ignore the first one. What’s the point?”