Have you ever heard of people using the phrase "rate of speed" before? I have, mainly on TV during one of our local news. Usually it is during a description of some vehicular traffic incident, and some vehicle was described as moving at a "high rate of speed". What they really want to say is simply that the vehicle was moving very fast, but somehow, they think saying "high rate of speed" sounds "sexier".
This, of course, is rather inaccurate. Typically, when say say "rate of something", we usually mean the time rate of change. In calculus, it is d/dt of something, i.e. the time derivative. So when one say "rate of speed", one is actually saying ds/dt, where s is speed. This is ACCELERATION!
Now there's nothing wrong with this if the newscasters actually did intended to say acceleration (which begs the question on why they don't just say "acceleration"?). But more likely, they wanted to say "speed". So really, transposing "speed" into "rate of speed" is not only non-economical in terms of words to say, it is also no longer correct.
So, if you write for some news broadcast, and you want to say that a vehicle moves very fast, just say "high speed" and NOT "high rate of speed". If your producer or proof reader disagree, ask him/her to open a physics textbook.