The Time is Right

When the hands of a clock are showing 3 o'clock, they form a right angle. (See picture at left.)

When will be the very next moment at which the hands again form a right angle?

NOTE: Express your answer in exact form, no decimal approximations accepted.

HINT: the answer is not 9 o'clock.

Bonus: At 9 o'clock, the hands again form a right angle (see diagram at right).

However, the angle indicated is called a reflex angle. It measures 270°. When will be the very next moment at which the hands form an angle of 90°?

NOTE: Before writing out your answer, please check our Guide lines for Writing POW Answers.