To find: The time taken by Karen to paint the house alone.
The time taken by Karen to paint the house is 3 hour.
Given:
Betty takes 6 hour to paint the house and if they work together than they take twothirds the time taken by Karen.
Calculation:
Let the time taken by Karen to paint the house be x.
Tabulate the given information into the language of algebra.
In words  In Algebra 
Time taken by Karen  x hr 
Time taken by Betty  6 hr 
Time taken by both 

Work done by Karen 

Work done by Betty 

Work done by Karen and Betty 

Model the equation for the above information.
Simplify the above equation for x,
Thus, the time taken by Karen to paint the house is 3 hour.