Final answer:
The lengths of the two pieces are 49 inches and 147 inches.
Step-by-step explanation:
To find the lengths of the two pieces, let's assume that the length of the shorter piece is x. According to the problem, the longer piece is 3 times the length of the shorter piece, so its length would be 3x. The total length of the board is 196 inches, so we can write the equation x + 3x = 196. Simplifying this equation, we get 4x = 196. Dividing both sides by 4, we find that x = 49. Therefore, the lengths of the two pieces are 49 inches and 3(49) = 147 inches. So the correct answer is B. One piece is 49 inches, and the other is 147 inches.