Try looking at it like this:
The airplane moves forward from thrust at 10mph, the runway goes aft at 10 mph and the airplanes wheels are turning over at 20 mph. Lets assume liftoff speed is 70 mph. Then when the airplane is going 70 mph forward, the runway treadmill is going aft at 70 mph and the airplanes wheels are rotating at 140 mph, and the airplane flies away.
The airplane moves forward from thrust at 10mph, the runway goes aft at 10 mph and the airplanes wheels are turning over at 20 mph. Lets assume liftoff speed is 70 mph. Then when the airplane is going 70 mph forward, the runway treadmill is going aft at 70 mph and the airplanes wheels are rotating at 140 mph, and the airplane flies away.