Final answer:
Using the equation y = 3x + 5.2 and substituting the marathon distance of 26.2 miles for y, it's determined that Tori will need 7 weeks of training to be ready to run the marathon.
Step-by-step explanation:
To calculate the number of weeks Tori needs to train in order to run a marathon, we use the given linear equation y = 3x + 5.2, where y is the number of miles she can run and x is the number of weeks she has been training. We want to find the value of x when y is equal to the marathon distance of 26.2 miles. By substituting 26.2 for y in the equation, we get 26.2 = 3x + 5.2.
Solving for x, we subtract 5.2 from both sides to get 21 = 3x, and then divide both sides by 3 to find x. Therefore, x equals 7. This means Tori will be ready to run the entire marathon after 7 weeks of training.