HANDS ON A CLOCK FACE PROBLEM?

At 12:00 noon sharp both the minute hand

and the hour hand point straight up and

are on top of one another on all round 12

hour clock faces.

One hour later the minute hand has made

a full circle and is again straight up at

the 12. During that same hour the hour

hand has moved and is now on top of the 1.

Exactly what time will it be when the

minute next hand catches up with the hour

hand and they line up precisely again?

Please round your answer to the nearest

millisecond and use the form hh:mm:ss.sss.

Hint: it will NOT be 01:05:00.000 since

the hour hand will have moved during the

5 minutes the minute hand took to get to

the 1 where the hour hand was.