To solve this problem using unit rates, we can first find the rate at which Wayne's office recycles paper per week and then use that rate to determine how many weeks it will take to recycle 10 kilograms of paper.
Given:
Total paper recycled over 3 weeks = 6 kilograms
First, find the rate of recycling per week:
Rate per week = Total paper recycled / Number of weeks
Rate per week = 6 kilograms / 3 weeks
Rate per week = 2 kilograms/week
Now that we know the recycling rate is 2 kilograms per week, we can find out how many weeks it will take to recycle 10 kilograms of paper:
Number of weeks = Total paper to be recycled / Rate per week
Number of weeks = 10 kilograms / 2 kilograms/week
Number of weeks = 5 weeks
So, it will take Wayne's office 5 weeks to recycle a total of 10 kilograms of paper at a rate of 2 kilograms per week.