Tire Calibration

I posed a question to my "lower" pre-calc class today.  I started by telling them that the problem was really hard and that I wanted to determine who the "smarty-pants" in the class were.  This is a class full of students who won't quite make it to Calculus.  Most of them have trouble understanding material, they prefer to memorize.  So I take special care of this class and make sure I show them why.  I rarely teach them any tricks as they will rely of those and forget why.  Anyway, below is the problem and I am proud to say that about half of the students got a correct solution and beyond that they were proud of themselves too.

As you are driving down a road in your car you see that your speedometer shows a velocity of 45 mph.  However, you know that you have the wrong tires on your car.  The tires you have on have a radius of 18 inches and your tires should have a radius of 16 inches.  This means that even though your speedometer reads 45 mph, you are truly going faster.  What is the true linear speed of your car?  Show and explain all of your work.