Final answer:
The shorter piece of the string is 3 feet long, and the longer piece is 10 feet long. These lengths satisfy the condition that the longer piece is 4 feet longer than twice the length of the shorter piece, with the total length of the string being 13 feet.
Step-by-step explanation:
To solve this problem, we need to set up an equation based on the given information, which tells us that the longer piece of string is 4 feet longer than twice the shorter piece. Let's call the shorter piece of string x feet long. Therefore, the longer piece would be 2x + 4 feet long since it is 4 feet longer than twice the length of the shorter piece.
The total length of the string is 13 feet. We can represent this as an equation: x (shorter piece) + 2x + 4 (longer piece) = 13 feet (total length). When we solve this equation for x, we get the length of both pieces.
Combining like terms, we get 3x + 4 = 13. Subtract 4 from both sides to get 3x = 9. Dividing both sides by 3, we find that x = 3. So, the shorter piece is 3 feet long, and the longer piece is 2(3) + 4 = 10 feet long.