Henry used 2/3 of the length of a board to make a box and 1/4 of the original length of the board to repair a step. The remaining piece of the board was 2 feet long. How many feet long was the original board?

\dfrac{2}{3}+\dfrac{1}{4}=\dfrac{8}{12}+\dfrac{3}{12}=\dfrac{11}{12}, so that 2 feet left over represents \dfrac{1}{12} of the board. If \dfrac{1}{12} of the board is 2 feet long, then the whole board was 24 feet long.

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