Starting from the time on this clock, when will the hands NEXT be at right angles?

The clock shows 3:05; the hands were at 90° at 3:00. Next the minute hand must be 90° AHEAD: 5.5m − 90 = 90, so m = 180 ÷ 5.5 = 32 8/11 min past 3. (16 4/11 is when they overlap; 30 min forgets the hour hand moves.)