Consider a simple polygon P containing disjoint convex polygons each of which shares an edge with P. The Zookeeper's Problem then asks for the shortest route in P that visits all convex polygons without entering their interiors. Existing algorithms that solve this problem run in time super-linear in the size of P and the convex polygons. They also suffer from numerical problems. In this paper, we shed more light on the problem and present a simple linear time algorithm for computing an approximate solution. The algorithm mainly computes shortest paths and intersections between lines using basic data structures. It does not suffer from numerical problems. We prove that the computed approximation route is at most 6 times longer than the shortest route in the exact solution.