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I give no formulas, because I'm afraid that people use them out of context. They become what I call "zombies," mindlessly using equations and getting themselves all the wrong answers. For example, in that equation for distance/time: 2xy/(x+y), some people will say to themselves, "Perfect! That's all I need to know." Let's look at a rather simple problem:
A car goes 25 miles per hour for 10 km, then goes 50 miles per hour for another 10 km (technically this is impossible, the car would have to accelerate from 25 to 50, but whatever). What's the average speed of the car? Now, by using the equation above, you get 33.3, while the answer is clearly 37.5 miles per hour.
I think a lot of people feel a sense of security when given an equation, because they think that that's all there is to it, when it requires thinking. Also a way lots of high school students approach math class--remember this formula, remember that equation, without any understanding of how basic equations arise and how they can be used.
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