There can be only two possibilities:<br>1. In case the plane and the car were moving in the same direction the plane was indeed flying with slower speed than the car.<br>2. In case the plane was flying with greater speed than the car the plane was going in some other direction. The component of velocity of the plane in the direction of motion of the car matters here which is lesser than the velocity of the car in your case.<br>Another way of seeing is (as the OP said the plane and the car were pretty much going in the same direction):
![enter image description here][1]<br>The car **C** can only see the background object **B** as coming out from the mouth of the plane **P** if the distance traveled by the plane **PQ** is smaller than the distance traveled by the car **CD** and the car will pass the plane also if **B**,**P** and **C** are always in straight line then the plane is traveling slower than the car and the car will pass the plane at the place where **BPC** is perpendicular to the ground. If the plane travels equal to or faster than the car then the car would see the background object **B** as coming out from the tail of the plane.


  [1]: https://i.sstatic.net/EZ8Bn.jpg