We can use unit rates to solve this problem. We know that Luther prepared 18 kilograms of dough after working 6 hours, which means he prepared:
18 kg / 6 h = 3 kg/h
This is Luther's unit rate of dough preparation, which means he prepared 3 kilograms of dough per hour.
To find out how many hours Luther worked if he prepared 21 kilograms of dough, we can set up a proportion using his unit rate:
3 kg/h = 18 kg/6 h
We can simplify this proportion by multiplying both sides by 7:
21 kg/h = 126 kg/6 h
Now we can see that if Luther prepared 21 kilograms of dough, he must have worked:
6 h * (21 kg/h ÷ 18 kg/h) = 7 hours
Therefore, Luther worked for 7 hours if he prepared 21 kilograms of dough.