Newton's third law.
The force acting on the car from pulling the trailer equals the force acting on the trailer from being pulled by the car.
A rope is a hard thing to conceptualise. But think of a simpler bit equivalent scenario, a car pulling a trailer by a chain. Now apply Newton's third law to every adjacent pair of chain links, and you'll see how the (same) force - tension - is transmitted from the car to the trailer. A rope is essentially the same.