Try dividing both sides by ab, and see if you can make the inequality equivalent to one that is known to be true. Then you can reverse your steps to...
The reason the average speed will be lower than 20 mph (the average of the two speeds) is that the rider will spend more time at the lower speed, so...
If x^2 + 3 is not in brackets, and the expression is written in-line as you did, then it is not a numerator! What you wrote means x^2 + \frac{3}{4} +...
It's written a little oddly, but makes sense. I can show you how to do it in Excel, but since you want to understand it first, the best way to start...
I've seen this problem before, given to students at this level, probably intended to be solved by orderly trial and error, with a little intelligence...
I was a software engineer for many years, and have been teaching at a community college since 2004. Since 1998, I was a part of Ask Doctor Math (http://mathforum.org/dr.math/ and now http://themathdoctors.org/).