Final answer:
The car with mattresses on its roof encounters greater aerodynamic drag than the car without, causing its engine to consume more gasoline to overcome this increased resistance.
Step-by-step explanation:
The scenario described involves the physics concept of aerodynamic drag, which is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. In this case, the cars are traveling through the air, which acts as the fluid. The car with mattresses on its roof encounters greater air resistance or drag, compared to the car with nothing on its roof. This increased drag forces the car's engine to work harder, thus using more gasoline to maintain the same speed and reach the destination.
Moving objects experience drag due to the air particles that they have to push out of the way as they move. The more surface area an object has, the more air particles it needs to push aside, leading to increased resistance. This resistance is what we refer to as drag. Drag force increases with the square of the velocity, which means that as a car goes faster, it has to overcome a significantly greater force. When a car has a large, bulky item like mattresses on its roof, it increases the surface area exposed to airflow, remarkably increasing the drag force.
The increase in drag due to the mattresses causes the car's engine to burn more fuel to overcome this resistance, hence explaining why the car with the mattress on top used more gasoline. This is an important consideration in the design of objects that move through fluids, including air, and is a relevant concept in vehicle design for fuel efficiency.