I'll bet Bob can chime in on this with some hard numbers-
That's a good bet.

A mass-reaction system, like a rocket engine, is a very poor way to drive a vehicle. It is much better to use a mechanical system that transfers force directly to the ground, such as through drive wheels.
Think of it thing way… Suppose you are sitting on a small wheeled cart. Is it easier to propel yourself along by placing you hand on the ground and giving a push, or by throwing rocks to generate momentum thrust?
Suppose we are traveling on the highway at 65 MPH in a fairly typical sedan with the following measurements:
Curb Weight: 3,000 pounds
Driver & Cargo: 200 pounds
Frontal Area: 22 square feet
Drag Coefficient: 0.35
There are two forces we have to overcome: rolling resistance and aerodynamic drag. At highway speed on good tires, the rolling resistance is about 0.008 times the weight of the car. Drag can be calculated from the
drag equation.
In this example the rolling resistance is 25.6 lb and the drag, at sea level, is 83.2 lb. If we are using a rocket engine, we must therefore supply a thrust of 108.8 lb to maintain a constant speed of 65 MPH.
If we’re going to use a rocket in an everyday passenger vehicle, we need to keep the complexity of the system to a minimum. Therefore, let’s assume we’re using a monopropellant engine rather than a more complicated bipropellant engine. We’ll get the best performance from hydrazine, but it is very toxic and dangerous. More likely we’ll use hydrogen peroxide or nitrous oxide. Hydrogen peroxide can be a bit unstable, but it is liquid at room temperature and is not too dangerous to handle (you’ll need heaters in the winter to keep it from freezing).
The specific impulse will depend on the engine chamber pressure and the hydrogen peroxide concentration. The nozzle will have an expansion ratio optimized for sea level operation. Best case, I think we might get an ISP of about 120 seconds.
At 108.8 lb thrust and an ISP of 120 sec, the fuel consumption rate is 0.9067 lb/s. At 65 MPH it takes 55.385 s to travel one mile, therefore consuming 50.2 lb of fuel. Hydrogen peroxide weighs 12.0 lb/gallon, so we’re burning 4.18 gallons to go one mile. Our fuel economy is a dreadful 0.24 MPG!
Even if we use a high-pressure bipropellant system, our fuel economy is still lousy. Suppose we could somehow get an ISP of 300 s, we’re still managing only 0.60 MPG.
(Note that these calculations assume constant mass. In reality our mass is decreasing as the engine burns fuel.)