How can calculus be used to solve a snail kinematics problem?

[brushman]

Homework Statement

Three small snails are each at a vertex of an equilateral triangle of side 60 cm. The first snail sets out towards the second, the second towards the third, and the third towards the first with a constant speed of 5 cm/min. As they go they always head towards their respective target snail. How much time has elapsed and what distance the snails cover by the time they meet? What is the equation of their path? If the snails are treated as point-masses, how many times does each circle their ultimate meeting point?

The Attempt at a Solution

I'm having trouble starting this problem. I drew all the pictures and have it well visualized. I know the starting speed is 5 cm/min towards the adjacent slug so I drew the vector, and after t = 0 this vector starts changing direction.

I guess I have to use calculus but I don't really know in what way.

Can someone give me a hint on how to start this?
Thanks.

 

[CompuChip]

I am tempted to set up a system of differential equations here, e.g.
$$\vec x_1'(t) = 5 \hat x_{12}(t)$$
where
$$\hat x_{12}(t) = \frac{\vec x_2(t) - \vec x_1(t)}{\left\Vert \vec x_2(t) - \vec x_1(t) \right\Vert}$$

But for an introductory physics class, that seems a little to complicated. So maybe you can give some more information on what subject you are covering, what equations you are supposed to use, etc.

 

[brushman]

This is a calc based Physics I class. It's a "challenge" problem. It shouldn't need any more then basic calculus to solve.

I figure if the snails go straight to their meeting point without circling it at all, then their path could be described as an arc length of $(60/360)2\pi r$. However, I don't know if it is actually a perfect arc length or if it just looks like it, and it only works if the snails don't circle the point at all.