Sophia is in charge of planning an annual triathlon in her city. The triathlon will consist of three distinct sections, as described below. Section 1: A swim accross a part of Sunset Lake.
Section 2: A bicycle ride through the new city park.
Section 3: A run through downtown that ends at City Hall
The organizing committee for the triathlon asks Sophia to follow these criteria:
1.- Eite athletes should be able to finish in 2 hours.
2.- The distance of the swim is 1/5 the distance of the run.
3.- The entire course covers a distance of 28 miles.
Sophia does some research on top triathlon finish times. She finds that, on average, elite athletes are able to swim at about 3 mi/h, bicycle at about 20 mi/h, and run about 10 mi/h. Sophia needs to determine a triathlon course based on these rates.
Task Description
Plan the triathlon by determining the distance for each part of the course.
Create a system of three linear equations to represent the criteria in this problem.
a) Write an equation that models the distances of all parts of the triathlon.
b) Write an equation modeling the relationship between the distances of the swim and the run of the triathlon.
c) Use substitution to write a new equation that models the distance of all parts of the triathlon, and solve it for the distance for the bicycle ride.