Answer: Let's assume the length of the shorter piece of the rope is "x" feet. Since the other piece is three times longer than the shorter piece, its length would be "3x" feet.
Now, we can set up the system of equations to represent the given information:
Equation 1: The total length of the rope is 63 feet.
x + 3x = 63
Equation 2: One of the pieces is three times longer than the other piece.
3x = x + 3x
Now, we can solve this system of equations to find the length of the short rope (x). By simplifying Equation 1:
4x = 63
Now, divide both sides by 4 to find the value of x:
x = 63 / 4
x = 15.75 feet
So, the length of the short rope is approximately 15.75 feet.