This is a problem about optimizing a particular type of human-powered racing sport. A certain type of race occurs over a number of distances and speeds. For any given distance, the conventional wisdom is that the optimum performance is gained by a constant speed over the distance. The best performances of a large number of individuals has been plotted (including a large number of international champions), and for each individual the performances over different distances match very well the formula: 1/speed = a+b*ln(distance) (a,b are positive real constants particular to the individual) i.e., the inverse of the average speed (which is also the constant speed over the course) is equal to a+b*ln(total distance), where a,b are constant parameters specialized for each individual, although the parameter "b" is almost the same for all individuals. Thus, given a particular distance -- e.g., 5000 meters -- and the constants a,b, one can compute the speed down the course as 1/(a+b*ln(5000)). Now comes the question. I'm not convinced that the best racing strategy is a constant speed down the course. My gut feeling is that the optimum strategy involves going faster in the earlier part of the course, and slower later. The problem is: given a fixed distance -- e.g., 5000 meters, and fixed constants a,b -- what is the optimum speed over the entire course, for each different meter ? Do I even have enough information to decide the question ?