Image (somewhat distracting and annoying) via WikipediaProgress, from the starting line to the finish line, can occur in many different ways. Some start the race slowly but speed up toward the end, using reserves of strength; some jog along at a steady, even pace; still others virtually go into orbit at the start and burn out quickly to a vomitous, spleen-gripping, huff-and-puff walk.
Since we are Braintenance, we will choose a five kilometer race, in which three mathematicians are competing. Each has a distinct running pattern, strategy or (ulp!) formula for spanning the distance.
The question to answer regarding each runner is simply this: "How long will it take him (in minutes) to reach the finish line to receive his souvenir Tee-shirt?" Of course, these Ts are only available in one size...XXL.
Here's the lineup of our contestants:
Racer 1: This fellow runs (on average) one kilometer every 18 minutes.
Racer 2: This fellow starts the race at a rate of one kilometer every 12 minutes, but his pace declines by 10% per kilometer.
Racer 3: This fellow starts the race at a rate of one kilometer every 30 minutes (remember the tortoise and the hare?), but his pace increases by 15% per kilometer.
Okay, friends. Let the cerebration begin.
*Cerebrethon is indeed a Lingovation, and should be respected as such. It means "a competition involving the thought processes." Just click on the picture of our dear departed Uncle Albert, below, in order to learn more.
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