Treebeard's Stumper

The countdown to Science Fair continues, so here's an easy clock stumper. At 12:00, the hour and minute hands of a clock point in exactly the same direction. How many times does this happen in a 12 hour period? The next meeting is not quite 1:05, since the hour hand moves a bit during those first 5 minutes. So exactly when do both hands meet, figured to the nearest second? Is there an easy way to work this out? *Bonus* How many working days are there until Science Fair? (Hint: May 9 at 5:00 at the Middle School for science, BBQ, and softball! The clock is ticking....)
Answer
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