How long would it take a matter-antimatter GeV gamma ray laser photon rocket to get to Ross128b (11 light years away)?

I'm writing a colony story, and I want my ship to colonise Ross128b, which is 11 light years away from Earth. I need the characters to be alive when they get there, but it's okay if they've aged twenty years or so. I've been using G.G. Zel'Kin's 'A Photon Rocket', translated by Z. Jakubski for my research.

So apparently the speed of light is c = 299792 km/sec, and this type of rocket would travel at a third of it, 99 930 819.3 m / s, is this correct? Assuming the rocket is able to travel at this speed, how long would it take them to get to Ross128b? I'm aware of the s=d/t triangle but I'm awful at maths.

If they're travelling very fast, does that not mean that time will act differently for them than for the people back on earth? If they've been travelling for a week on the colony ship, how much time will have passed on earth? Will everyone they knew on earth be dead?

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How long would it take a matter-antimatter GeV gamma ray laser photon rocket to get to Ross128b (11 light years away)?

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