Chased by a lion and other pursuit-evasion problems

Since you're asking for a reference, perhaps this will do?

Wolfram Mathworld says the problem was listed by Rado in 1925. The reference is on the problem description page, here.

Here is a book on this type of problem

• Paul J. Nahin, Chases and escapes: the mathematics of pursuit and evasion, Princeton University Press, 2007.

it is also briefly mentioned in his other book "Euler's Fabulous Formula".

The book is Coffee in Memphis by Bollobas. It's the first problem, and there are loads more :

http://www.amazon.com/Art-Mathematics-Coffee-Time-Memphis/dp/0521693950