Question: Provide a step by step solution for the following math problem: Nate's dog can dig six holes a day. He digs for 14 days while Nate is on vacation. When Nate gets home, he starts filling in 9 holes a day, but the dog keeps digging 6 new holes every night. How many weeks does it take him to fill in all the holes?
Answer: 
First find the number of holes the dog digs while Nate is on vacation: 14 days * 6 holes/day = 84 holes
Then find the net number of holes Nate fill in each day: 9 holes/day - 6 holes/day = 3 holes/day
Then divide the total number of holes by the daily decrease in the number of holes to find the number of days Nate spends filling in holes: 84 holes / 3 holes/day = 28 days
Then divide the number of days by the number of days per week to convert the answer to weeks: 28 days / 7 days/week = 4 weeks