In the movie Passengers, the writers got a lot of details about how an interstellar starhip would work, from the heat shield to artificial gravity. But there was one detail that they only glanced upon in the movie that could change everything: the ship's speed.
In the movie, the awoken crew member Gus explained that the Avalon is traveling at 50 percent the speed of light.
As an object speeds closer and closer to the speed of light, relativistic effects (such as time dilation) will become significant on it.
When Aurora played back that video of her friend on Earth, her friend referenced the journey as a 120 year voyage; meaning that the travel time of 90 years is relative to the Earth's perspective.
Considering their speed and journey time, Homestead II could be placed at roughly 60 light years from Earth. If you calculated the level of time dilation and factored that in, the Avalon's entire flight time would be only 51.96 years. With 30 years of local travel time already cleared, the ship's remaining travel time would only be a mere 21 years.
If time dilation was factored in, wouldn't Aurora and Jim have made it to Homestead II alive and well even without sleeping most of the way?