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?
First find the number of holes the dog digs while Nate is on vacation: 14 days * 6 holes/day = <<14*6=84>>84 holes
Then find the net number of holes Nate fill in each day: 9 holes/day - 6 holes/day = <<9-6=3>>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 = <<84/3=28>>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 = <<28/7=4>>4 weeks
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