special relativity - How to achieve speeds faster than light?

So, I heard that all speed is relative. And that nothing can travel faster than light.

Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were to leave Earth at 0.6c in the opposite spacial direction.

Then the relative speed between the two ships would be 1.2c, which is greater than c. How would that work out? Maybe something with time dilation?

Answer

Galilean relativity and Special relativity use different identities to find the relative velocity of different objects. In classical mechanics, velocity addition formula of Galilean relativity can be used($v=v_1+v_2$). However, this doesn't apply to objects travelling at speeds close to $c$. At these conditions, relativistic addition formula gives much more accurate results. For inertial frames, this can be explained via Lorentz transformation.(Simply, each frame has different distance and time measures.) Therefore, the relativistic velocity-addition formula becomes; $$ v=\frac{v_1+v_2}{1+\frac {v_1v_2}{c^{^{2}}}} $$ Overall, you can say that special relativity gives us a more generalized equation to calculate the relative velocity.