I took this as a product design question and talked about isolating the problem. I mentioned various parts that could be causing it to slow down. I mentioned how once you determine the component to alter, you'd want to look at various solutions. I listed everything I could think of from refactoring code, database changes, installing data centers, routing tables etc. I talked about how we need to keep in mind the user base and determine the tradeoffs value by how much it affects the user base. I described a framework to develop the solutions iteratively through a/b testing.