:lol: The problem is just a definition of speed and where on the wheel we are talking about. From what I have read so far everyone has a pretty good handle of the physics. If you think the plane can move forward without breaking the rule (ie - measure speed at axle of wheels) then of course the plane can take off, because the wheels will just spin twice as fast as they normally would, but why wouldn't the question just say the "the speed of the plane" since it is the same thing. I see it more like a wheel trying to roll down an inclined treadmill where the treadmill speed is increased to keep the wheel from rolling downward. By matching speeds, the treadmill keeps the wheel locked in position, so the plane won't take off.
Which was covered in my lengthy post above. The ambiguity of the question lies in the wording about the speed of the wheels. Angular velocity can be described by the surface velocity of the wheel (it's a function of the wheel's radius) and therefore, surface velocity can be related to the plane's velocity. Realistically, there are two points to measure the wheel's velocity from, the top or the bottom. The top yields twice that of the plane, the bottom yields 0 (Wheels roll, don't slide). Using the word speed removes the directional element of velocity, making the actual direction unknown, but under both criteria, there is no force to stop the plane.
I think what you are getting confused about, is that the plane is stationary, the wheels aren't moving, therefore the conveyor isn't, and the system is balanced, so you can't move the plane without upsetting that equilibrium.