the shorter piece if the shorter piece is: x feet long

the longer piece is 3 feet longer than twice the shorter piece: 3 + 2x

a 15-foot piece of sting is cut into two pieces means:

x + 3 + 2x = 15

by solving we find

x = 4 ft

click here to see the step by step solution of the equation

15 - 4 = 11 ft

the lengths of the both pieces are 4 feet and 11 feet.