After the time shown, when will the hands next be at right angles?

The clock shows 9:05. At 9:00 the minute hand is $270^{\circ }$ behind. It next makes a right angle when it is $90^{\circ }$ behind, a gain of $180^{\circ }:\frac{180}{5.5}=32\frac{8}{11}$ min past $9.(16\frac{4}{11}$ is when they are opposite; $49\frac{1}{11}$ is when they overlap.)