A bus travels between two cities $A$ and $B$ which are $100$ miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a Uniform Distribution over $(0,100)$. There is a bus service station in city $A$, city $B$ and in the center of the route between $A$ and $B$. It is suggested that it would be more efficient to have the three stations at $25,50$ and $75$ miles, respectively, from $A$.
The question asks if the second arrangement is more efficient, I know how to calculate the probabilities, my intuition tells me that the second system is better, but can’t seem to come up with a way to conclusively state that either one will be better, can anyone help?