i need your help, math problem

<p>Hello, sorry it is an unusual post, but i need some help. On a recent math team problem at our school, many of the kids felt the answer was something, but it turned out to be something completely different, and I am having trouble understanding why the correct answer is correct, here is the problem, I hope you could help explain it:</p>

<p>The circumference of the larger crcle is two times that of a smaller circle, if the smaller circle is rolled around the edge of the larger circle, how many rotations does the smaller circle make. The imgae that was with it was two circles side by side, one smaller than the other, they were tangent to each other, and they were not inside eachother. So when rolling it has to go around the outside of the larger.</p>

<p>Here is what I did, but was wrong: C1 = 2(PI)r C2 = (C1)/2 = (PI)r
(C1)/(C2) = (2PIr)/(PIr) = 2. The correct answer is supposed to be 3, why?, thanks for your help.</p>

<p>weell it's simple
if they are tangent
the radius of othe ORBIT that the smaller circle travels around
would be raidus of larger circle PLUS radius of smaller circle.
there you go
so R1 + R2 = 2r2 + R2 = 3r2
so the circumference of the Orbit is 2 (pi) (3r2) = 6 (pi) (r2)
circumference of smaller circle = 2 (pi) (r2)
divide Orbit by cirumference = 3</p>

<p>your answer is when the larger circle IS the orbit of the smaller circle</p>