i'm not sure if this is a well known problem, or not, but anyway, the problem is:

we have a baby who starts in the center of a circle, and the mother walks around the edge of the circle. the baby always crawls directly towards the mother. the baby and mother have respective speeds $\displaystyle u$ and $\displaystyle v$ with $\displaystyle v < u$. The circle has radius $\displaystyle R$. How long does it take for the baby to reach its mother?