Will the rocket speed increase if the velocity of the outflow of gases relative to the rocket is less than the speed

Will the rocket speed increase if the velocity of the outflow of gases relative to the rocket is less than the speed of the rocket itself relative to the Earth?

The rocket speed will increase. This becomes obvious if we go to the reference system associated with the center of mass of the rocket along with the fuel.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.