The whole problem is confusing because
"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward."

Moving forward with respect to what? The conveyor belt? (you gt the
answer that it WONT take off), or the air? (you get the answer that it
WILL take off).

AMBIGUOUS!!!

(Cecil's answer assumes with respect to the air, and that is also how
he gets the tires going at twice the speed of the plane through the
air).