homework and exercises - Why does relativistic velocity subtraction produce a larger relative velocity than classically?

I got a question for homework saying that there were two rockets on a parallel track, heading towards earth. Rocket A was in front of Rocket B. Rocket A was travelling at a velocity of $0.75c$ from the frame of reference (FOR) of earth and Rocket B was travelling at a velocity of $0.5c$ from the FOR of earth. The question asked to find the velocity of Rocket A from the FOR of Rocket B.

I got an answer of $0.4c$, $$v_{AB}=\frac{v_a-v_b}{1-v_av_b/c^2}=\frac{0.75c-0.5c}{1-0.75c\cdot0.5c/c^2}=0.4c,$$

which both my teachers said was right.

I am confused because this velocity is greater than what I got using the formula for classical velocity addition ($0.25c$). For every other question I have done, the relativistic velocity is less than the classical velocity. I am wondering why the relativistic velocity is larger in this case?

Answer

If the two move in the same direction, you are dividing the classical result by a number less than one: $1-v_1v_2/c^2$, thus the result will be always larger than the classical. If they were moving in opposite directions, then the sign changes and you are dividing by a number larger that one, and thus you will obtain a result smaller than the classical one.

Both results are intuitive. Imagine that both are moving in the same direction close to c. Classicaly, the difference to you will be very small (let us say 0.00000001c), but they could be moving relative to each other to a speed close to c. If they move, instead, in opposite directions, at speeds close to c, the classical result will be closer to 2c, but they canot see each other moving at a speed larger than c, so the result will be less than the classical.