What some people aren't taking into account is that the hour hand (just like the other hands on this clock) is moving continuously. In other words, it won't just be stationary over the 12 from 12:00 to 12:59 and then suddenly jump to the 1 at 1:00. It continues to move at a rate of 1/12 of the arc of the circle (30 degrees) per hour.
if its 1 hour 5 mins after 12noon exactly its 13:05, theres no mention of the second hand...you are overcomplicationg it
&& the angle is 30degrees i think because a full circle is 360 degrees so you quarter it to make 90 and devide by 3...making the answer to the riddle 13:05 and 30 degrees.....thereis no need for long sums or pi...=S
I liked this riddle, a fun one to solve and a few different ways to do it (I used the speed of each hand around the clock).