Problem Solving

The easiest approach on this question is to use the combined work equation $$\frac{1}{A}+\frac{1}{B}=\frac{1}{A and B}$$ Where A and B are the time it would take each person (or machine, pump, printer, etc. depending on the question) to finish a job alone, and A and B is the time it would take both to finish the same job together.

In this problem, A will be the time it takes Robert to assemble the model car alone, B will be the time it takes Craig to assemble the model car alone, and A and B will be the time it takes the two of them to assemble the model car together. Plugging in the information from our equation gives: $$\frac{1}{20}+\frac{1}{30}=\frac{1}{A\ and\ B}$$ Then solving for A and B gives $$\frac{3}{60}+\frac{2}{60}=\frac{1}{A\ and\ B}$$ $$\frac{5}{60}=\frac{1}{A\ and\ B}$$ $$5\left(A\ and\ B\right)=60$$ $$A\ and\ B=12$$ So Robert and Craig can assemble the model car together in 12 minutes, and the correct answer is A.