Question

Darla is training for a marathon. She starts out running 1.5 miles and plans to add additional miles each week. Below is a screen shot from her fitness tracker app on her phone.

Part a: assuming that this pattern of running continues for darla, write an equation that could be used to find the number of miles she runs for any number of weeks.

Part b: to complete a marathon, you must run 26.2 miles. Using the table and/or equation, will darla be able to complete a marathon after 14 weeks of training?

Answer 1

Part A:
As we can see on this table, Darla run 3 miles the first week. Then she began running 1.5 miles each week (4.5 - 3 = 1.5; 6 - 4.5 = 1.5; etc...). Let x be the number of weeks. But since the first week is different from the others, we need to remove 1 from x.
The equation is: 1.5(x-1) + 3

Part B:
To know how much she can run in 14 weeks, we replace x by 14 in the previous equation.
1.5x + 3 = 1.5 * 14-1 + 3 = 1.5*13 + 3 = 22.5

So no, she can't run 26.2 miles in 14 weeks.