Solving the Ladybug's Clock Puzzle: Unraveling the Mystery

[kuahji]

Ok here is what the problem states in the book

"A ladybug settled onto the tip of a clock's minute hand. The minute hand is 12ft long. How far does the ladybug travel from 3:00pm to 3:20pm?"

I figured there are 30 degrees to every hour (divide 360 by 12). Then the 20 minutes would equal 10 degrees. However the example in the book says when you translate the problem in degress you get 120 degrees (twenty minutes is 20/60 or 1/3 an hour. 1/3 of 360 or 120 degrees acording to the book). I don't understand why I would want to calculate the problem for 120 degrees instead of 10...

Ok so I plug 10pi/180 into the arc of circle formula & end up with 2pi/3. The book ends up with 8pi. I end up with roughly 2.09 ft & the book ends up with roughly 25.13 ft. I don't understand... If the circumference of the circle is pi*d I get only get 75.39ft (2pi*12ft). The books answer seems like an aweful long distance to travel in just 20 minutes... Somethign doesn't seem right. Any ideas?

 

[Valhalla]

The ladybug is on the minute hand not the hour hand, hence 120 degrees per 20 minutes not 10 degrees (if it was the hour hand).

 

[kuahji]

thanks... usually when I can't figure something out it's some silly mistake as is the case this time.