How can philosophy and other related subjects help solve some of the world's problems? Or can't they?
What the study of philosophy and other academic subjects does is help people think more clearly and avoid vague generalization or jumping to conclusions based on insufficient data. Before asking about how to solve some of the "world's problems" a philosopher would ask you to think about what you mean by the world's problems.
For example, in considering whether income inequality is a problem, a philosopher would ask whether it is a problem for all people and why. The very rich might not consider it a problem, and certain extreme capitalists might simply consider it an inevitable result of competition, while for many of the poor, or for the compassionate, it would be a problem.
Even more profoundly, philosophers would ask us to consider why we think of problems materialistically. So, for example, some philosophers would state that since we can never entirely control external circumstances, that such circumstances are not in and of themselves problems, but rather that our attitudes problematize them. Even though we cannot control external events, according to Epictetus, we can control our own emotional responses.
Many religious and spiritual philosophers might say that this world is itself unimportant or illusory, and cannot really be a problem to the trained philosophical or religious soul.
Thus philosophy can help us attain inner peace whatever happens in the world, in a certain way solving problems for us.