Question 1012020
The answer will be 11 something, due to the wording, so we get to work solely in minutes (else wise there are a multiple number of answers).


The hour hand only moves 360/12 30 degrees an hour, and since there are 60 minutes in an hour, we have 1/2 degrees per minute. 

The minute hand, on the other hand (haha) moves at 360 degrees an hour, and since there are 60 minutes in an hour, we have 6 degrees per minute. 


If the two are to be on the opposite sides, they are 180 degrees apart. 11 o clock is 11/12*360=330 degrees, so the hour hand starts there. We now have an equation.


330+x/2=6x+180
*[invoke explain_simplification "330+x/2=6x+180" ]