In this paper, the target guarding problem, posed by Rufus Isaacs in his seminal textbook is revisited. Unlike the simplified version of the problem solved by Isaacs, optimal strategies are discussed for the pursuer and the evader having simple motions with different speeds. Analysis is also done for the case when the intercept occurs if the pursuer reaches within a certain distance of the evader, instead of a strict coincidence of their positions. The importance of the study is that, it is fundamental to building autonomous systems that would be used for protecting a target, for example, unmanned vehicles used in anti-poaching operations.