The ability of an astronaut to make it back to the lunar lander before running out of oxygen would depend on several factors, including the remaining oxygen supply, the rate at which the oxygen is escaping through the hole, and the distance between the astronaut and the lander.
Assuming the astronaut's suit is airtight apart from the one centimeter hole and the hole is not increasing in size, the primary concern would be the rate at which the oxygen is escaping through the hole. If the leak is small, it may take longer for the astronaut to deplete their oxygen supply, allowing them more time to reach the lander.
The duration of the available oxygen supply in an astronaut's portable life support system (PLSS) can vary depending on the specific mission and equipment. However, a typical oxygen supply in a spacesuit is designed to last for several hours. If the astronaut has a substantial amount of oxygen remaining, it increases their chances of making it back to the lander.
Assuming the astronaut is in close proximity to the lander, with only a short distance to cover, they would have a better chance of reaching it in time. However, moving in a spacesuit can be physically demanding, and the lunar environment poses its own challenges, including reduced gravity and the need to maneuver in a bulky suit.
In an emergency situation like this, time is of the essence. The astronaut should prioritize reaching the lander as quickly and efficiently as possible, while taking precautions to avoid further damage to the suit or the integrity of the helmet. They could potentially take short, controlled jumps or use other techniques to expedite their movement towards the lander.
It's important to note that this scenario assumes the astronaut maintains their composure and acts swiftly. In real-life situations, emergency procedures and protocols are in place to handle such contingencies, and astronauts undergo extensive training to ensure they can respond effectively to emergencies.
Overall, whether the astronaut can make it back to the lunar lander before running out of oxygen would depend on the specific circumstances of the situation, including the factors mentioned above.