bodner088

In our last titillating post, we briefly discussed the ways in which different runners pace themselves to arrive at the finish line of a 5 Kilometer race . We choose three mathematicians to compete, each one using his own approach to pacing the his way to the finish line. The award for the fastest and first to arrive at the finish (amid cheers, popping champagne corks, autograph requests and other of the accoutrements accompanying a heroic feat) was a free XXL Tee- Shirt (with the event sponsor's name, Tanks-A-Lot Cesspool Cleaning Service , " We Keep You Running ". Here we go.... ---------------  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?" ...

Image ( somewhat distracting and annoying ) via Wikipedia Progress, 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 ki...