THE GREAT RACE
Summer and Jackie are on a floating platform on a lake and decide to race to the snack bar. Summer is a better swimmer and Jackie is a better runner. They make a bet that whoever loses the race has to buy the snacks. Summer swims at a rate of
In order to optimize the time it takes to reach the snack bar, both girls will swim part of the way and run part of the way. Notice that the running part is horizontal but the swimming part is diagonal.
Since distance = (rate)(time),
Before you apply Calculus to optimize, write a geometric equation describing the distance,
Convert the distance equation into time equations,
Use the eTool below to explore the problem.
Click on the link to the right to view to full version of the eTool. Calc 6-107 HW eTool