Final answer:
The longer piece of the rope must be 24 feet long.
Step-by-step explanation:
To find the lengths of the two pieces of rope, we can set up an equation. Let x represent the length of the shorter piece. The longer piece would then be 2x. The sum of the lengths of the two pieces should be equal to the total length of the rope: x + 2x = 36 feet. Simplifying the equation, we have 3x = 36. Dividing both sides by 3, we find that x = 12. Since the longer piece is twice as long as the shorter piece, it must be 2 * 12 = 24 feet.