Final answer:
To determine the lengths of the two pieces of the board, we can set up a proportion using the given information and solve for the unknown lengths. The longer piece is 18 inches and the shorter piece is 12 inches.
Step-by-step explanation:
To solve this problem, we can set up a proportion using the given information. Let the length of the longer piece be x and the length of the shorter piece be (2/3)x. Since the total length of the board is 30 inches, we can write the equation: x + (2/3)x = 30. Combining like terms, we get (5/3)x = 30. Multiplying both sides by 3/5, we find x = 18 inches. Therefore, the longer piece is 18 inches and the shorter piece is (2/3)(18) = 12 inches.