I was doing a problem in Griffith's "Intro to Electrodynamics" concerning a clairvoyante and her twin brother:

 

Sophie Zabar, clairvoyante, cried out in pain at precisely the instant her twin brother, 500 km away, hit his thumb with a hammer. A skeptical scientist observed both events from an airplane traveling at 12c/13 to the right. Which event occurred first, according to the scientist? How much earlier was it?

 

I did it using the Lorentz transformation. I don't know if I did it correctly or not so I was wondering if someone could help me make sure I did this correctly.

Well, what did you do and what answer did you get?

Well I just set event B (for brother) as x(b)=0 and t(b)=0 and event S (Sophia) as x(s)=500 km and t(s)=0 and v(sc)=12c/13 for the scientist. I used the Lorentz transformation and found that the scientist "sees" event S at 541 km but 4 microseconds before the brother hurts his thumb.

Well, what did you do and what answer did you get?

Did I do this problem the correct way?