An algorithm that computes the exact solution to the general Zookeeper's Problem in O(n^2) time has been published. There is also an algorithm that solves the restricted Zookeeper's Problem in O(n\log n) time. In this paper, we give a simple O(n) time algorithm for computing an approximate solution to both the general and the restricted Zookeeper's Problem. Such an approximation route is at most a factor 6 times longer than the shortest route in the exact solution.