Question

sariah has just begun training for a half-marathon, which is 13.1 miles. since she was on vacation, she started the training program later than the rest of her running club. There are 6 weeks of training runs remaining before the race.

In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the train program for her to get up to half-marathon distance?

Describe how you would solve this problem using Polya’s four-step problem-solving method. Complete each task as part of your response. Be sure to number task 1-task 4 so that your instructor can tell which part you are answering.

1. understand the problem

2. formulate a plan
task 2: identify the model you would use to represent the problem and explain why you chose the model.

3. implement the plan

4. review the results

1. There would not be enough time to reach the half marathon distance.

### Would there be enough time to reach the half marathon distance?

The distance run in a week can be represented with a linear equation. A linear equation is an equation that has a single variable raised to the power of 1.
The linear equation that would be used to represent the distance run would be in the form:
Miles run in a week = miles run the previous week – increase in miles
Increase in miles = 6 – 4.5 =  1.5 miles
Miles run in the fourth week = 1.5 + 6  = 7.5 miles
Miles run in the fifth week = 7.5 miles + 1.5 miles = 9 miles
Miles run in the sixth week = 9 + 1.5 = 10.5 miles
There would not be enough time to reach the half marathon distance because in the sixth week she would be able to run 10.50 miles