If you believe that you will have evidence in the future that enables you to decide between in front of you and in back of you, driving slowly may be the optimal decision. For instance, assume you think that the hotel can be in one of two locations, either a specific spot ahead of you or a specific spot behind you, and you are not equidistant from those two locations, you will receive evidence a fixed time in the future, and if you travel at half speed you will receive the evidence when you are equidistant between the two possible locations. Then travelling at any speed (that doesn't pass the hotels) will not change the average distance to the hotel at the moment you find the evidence, but travelling at a speed designed to put you in the middle when you get the evidence will reduce the worst case scenario without affecting the average. Therefore you should travel at half speed. Furthermore, it may reduce the average as well if the chance of receiving evidence varies on how much total distance you have travelled (seeing a landmark that you know is past or before the hotel would be evidence, for instance).

Of course I've defined this scenario in a bunch of arbitrary ways, but they aren't really necessary to make the optimal result travelling at half speed, they just make the optimality easier to demonstrate.