Your quarter horse, is about to begin running the barrels. He starts to gallop. When a horse starts to gallop, he needs an immediate source of energy. This energy is found in the very small amounts of stored ATP and phosphocreatine. However, these supplies are quickly exhausted (within seconds). Your quarter horse's powerful, predominately Type IIb muscles, have by now started the process of producing energy by anaerobic glycolysis. This process is in at its peak within 60 seconds – with the job that your horse is doing now, this is all the energy that he needs. Because your quarter horse has a high proportion of fast-twitch muscles that are meant to move into gear quickly and anaerobically, and produce great strength and power, he is innately suited for many of his jobs, such as the quarter-run, barrel-racing, and calf-roping. However, these muscles can't sustain this process for more than a half a mile, so your quarter horse can't keep up the pace over a longer distance.
Imagine a different scenario – your thoroughbred racehorse is in the starting gates, facing a mile and a half course, instead of several hundred yards of sprinting. What happens? Well, he starts the same way that the quarter horse did under full throttle. But now, he must sustain his effort for longer than is possible with anaerobic glycolysis. The thoroughbred, by birth, has a higher proportion of slow twitch, oxidative, Type I and Type IIa muscles. Within one minute, the slower, but more efficient process of aerobic glycolysis has begun to supplement his efforts. Although aerobic glycolysis is much more efficient, it is not as fast a method of producing energy, so at this point, the pace starts to slow. Although the thoroughbred still keeps up an amazing speed over the last 3/4 of the race, he is physically incapable, no matter what his training regimen, of completing the entire race at a sprint.
Now, to stretch your mind a little further, imagine an Arab competing in a 100 mile endurance race. He needs more energy than even aerobic glycolysis can afford, but he doesn't need the powerful, short-term speed of the quarter horse, or even the pace that the thoroughbred can maintain for a mile to a mile and a half. Instead, he needs to be steady and sure for a truly impressive distance. The endurance horse needs a fuel that is in plentiful supply, but he doesn't need instant delivery of fuel – and this is found in the form of oxidation of fats. This process is slow, but extremely efficient. Even in a fit, muscular looking horse, there are enough body stores of fat to last for a very long time. Thus, the endurance horse will rely primarily on his Type I muscles to (relatively) slowly but very steadily power him through his grueling task.