Alana and Kelsa are training for a marathon. To prepare for this marathon they have been training and tracking their progress periodically.

In the first week of training Alana ran an average of 20 minutes per mile. Later, in week seven of training she ran an average of 14 minutes per mile.

In the first week of training Kelsa ran an average of 15 minutes per mile. Later, in week five of training she ran an average of 13 minutes per mile.

Assuming that Alana and Kelsa continue to train and improve their times at the same rate your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 43 weeks. To complete this task follow the steps below.

1. Determine the equation of a line in standard form that represents Alana’s training progress. Her progress corresponds to the points (1, 20) and (7,14).

2. Determine the equation of a line in standard form that represents Kelsa’s training progress. Her progress corresponds to the points (1, 15) and (5,13)

3. Solve the system of equations (you must show all your work to receive full credit).

4. In which week will Alana and Kelsa have the same average minutes per mile?

5. If Alana and Kelsa continue to train until week 30, what will their times be?

6. Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed?(Hint: look at question 5). What do you think this says about problems in the real world? Justify your thoughts in 3-4 sentences.