Hi, Alexandria!

I'm really, REALLY bad at chemistry/physics and math. ... Practice hasn't really seemed to help too much beyond working problems. Give me an equation and variables and I can do the math. But I can't EXPLAIN anything, or apply it to non-obvious problems involving it.

Okay... I am one of those people who is really good at math. Of course, I cannot be certain, but I suspect that the trouble here might be that you failed to grasp some essential point way, way back at the early stages of your mathematical education.

So, let's see how you handle a non-obvious problem. In answering this question, I'd like you to show me, as far as possible, your entire reasoning process, start to finish; the more information you can give, the more helpful my further responses can be.

The question is as follows: John is on his way to an important meeting; he has to be there at noon. Before leaving home, he has calculated what his average speed has to be to arrive at his meeting on time. When he is exactly half-way to his destination, he calculates his average speed so far, and to his dismay he finds that it is half the value that it needs to be.

How fast does John need to travel on the second half of his journey in order to reach his destination on time?