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For example: In one problem we were given a spaceship leaves earth to a star distance x away(in the Earth reference frame), the spaceship has a velocity of y with respect to the earth. How long does it take to get to to asteroid in the Earth reference frame? The ships? This you can use simple time dilation.

Our next problem was: Frame S' has a speed of x relative to S, clocks are adjusted so that t'=t=0. A photon is emitted in S at x=0 and absorbed at x=50 m, what time does this event occur in S'? This you need to use the full Lorentz transformation.

I am sure it is pretty simple to understand when and why you can use one or the other but I am a bit confused. Thanks for any help!