Light travels at 300,000 km/s. Always, forever, no matter who is observing it.

So imagine Alice is aiming a laser pointer into space. She fires a pulse of light. The photons in the pulse are traveling up at 300,000 km/s.

Now imagine Bob is flying by on a rocket traveling at 100,000 km/s in the same direction as the laser pulse. Every second he should observe the laser beam traveling away him by only 200,000 kilometers, right?

Nope. He still observes the pulse traveling 300,000 km away from him every second.

But if he’s traveling at 100,000 km/s away from Alice, how is Alice ALSO observing the beam traveling at 300,000 km/s?

The answer is that Bob and Alice are experiencing time differently. When Alice looks at Bob, Bob appears to be moving at 2/3 speed, whereas Bob sees Alice moving 3/2 faster than him. That way, light still travels at 300,000 km per second for both of them. It’s just that “one second” is longer for Alice than it is for Bob.