Yeah, I came up with the answer that everybody else did too. And I was heavy into amateur astronomy a few decades ago and I know about sidereal time. But I failed to recognize or apply that concept when solving this problem. I guess my brain is just too old and worn out these days.
Luckily this question didn't hit the SAT until years after I had taken it (I got 800 on the math part back in '75). I admit, I would have gotten it wrong (although they did eventually throw the question out of the SAT test score, since they didn't give you a choice for the correct answer, so a wrong answer didn't count).