Final answer:
To find the lengths of the two pieces, set up a system of equations. The lengths of the two pieces are 19 inches and 38 inches.
Step-by-step explanation:
To find the lengths of the two pieces, we can set up a system of equations. Let x represent the length of the shorter piece. Since the longer piece is two times the length of the shorter piece, its length is 2x. The sum of the lengths of the two pieces is equal to the length of the original board, so we have the equation:
x + 2x = 57
Combining like terms, we get:
3x = 57
Dividing both sides by 3, we find that x = 19. Therefore, the lengths of the two pieces are 19 inches and 38 inches.