Final answer:
The only hope for the Apollo 13 crew to return alive was to utilize the Lunar Module (LM) as a lifeboat, which required modifications to support three astronauts for a longer period of time.
Step-by-step explanation:
The only hope for the Apollo 13 crew to return alive was to utilize the Lunar Module (LM) as a lifeboat. Due to an oxygen tank explosion, the Command Module (CM) was disabled and rendered uninhabitable. The LM, designed to support two astronauts for a shorter duration, had to be modified to support three astronauts for a longer period of time. The successful implementation of this plan allowed the crew to use the LM as a shelter and propulsion system to navigate around the moon and safely return to Earth. The crew's survival and return were also due to the ingenuity of the NASA engineers who devised makeshift solutions to unexpected problems, an example of overcoming functional fixedness under intense pressure. The team on the ground had to work with materials available to the astronauts on board to create work-around systems, including fashioning a carbon dioxide filter using duct tape and other materials. The success of these remarkable efforts in face of dire circumstances illustrates the importance of adaptability, teamwork, and innovation in space exploration.