<human>:  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?
<bot>: How many holes does the dog dig while Nate is on vacation? ** First find the number of holes the dog digs while Nate is on vacation: 14 days * 6 holes/day = <<14*6=84>>84 holes
How many holes does Nate fill in each day? ** Then find the net number of holes Nate fill in each day: 9 holes/day - 6 holes/day = <<9-6=3>>3 holes/day
How many days does it take Nate to fill in all the holes? ** 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
How many weeks does it take him to fill in all the holes? ** 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
#### 4