Problem
Two starships, docked to one another, find themselves caught in a strange space manifold that is pulling them along in space in a particular direction at a particular constant speed. They cannot escape the manifold, but they can travel along the manifold in either direction.
The two captains consult one another and decide on the following plan: Starship A will travel at full power in the opposite direction that the manifold is pulling (think against the current of a river), while Starship B will travel at full power in the same direction that the manifold is pulling (think with the current of a river). The two ships have equal power, leave at the same time, and each move at constant velocity - that is, we will ignore acceleration and deceleration.
i. When they start off, one ship leaves a probe as a buoy, which is pulled along the manifold at the speed the manifold is moving. After two hours, the captains realize this isn't helping, and they simultaneously reverse course and head back toward one another.
ii. Which starship will reach the buoy first? (I've had two friends say they reach the buoy at the same time, one said ship B will make reach the buoy first and ChatGPT said ship A...so im looking for further expert opinion)
iii. What is the answer to the question of the end of the puzzle? Explain your reasoning. Can you please explain with mathematical formulas/notation used to prove the answer.
iv. Describe how you considered Rule 3 from the Puzzle-Based Learning textbook: Please clearly identify your model and all its parts (variables, constants, objective, etc.).