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Let's say that humans find a habitable planet 100 light years away and begin to build a ship that goes in the speed of light to get there. they fix hibernation pods in the ship so that humans could reach the planet without aging. while the ship is on the voyage two hibernation pods break and two people wake up(You know where I am getting right the movie PASSENGERS) and they still have 80 light years to go. but they find a medical robot to simulate the hibernation pod.Can you as the person in the situation find a mathematical way to reach the habitable planet alive and young as possible for both of you by sharing the medical robot.

person 1 age = 30
person 2 age = 30
life expectancy = 80

Kunal Mehta
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    I assume it is possible if one person sleeps for 40 years and then the other sleeps for the remaining 40 years. – For the love of maths Dec 27 '17 at 10:17
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    100 light years would be intragalactic, it's 25,000 lightyears to the next galaxy, Canis Major Dwarf. –  Dec 27 '17 at 10:25
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    Sorry but I fail to find any difficulty. $30+80/2=70$. Or am Imissing something ? –  Dec 27 '17 at 15:50
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    Also note that time freezes when you travel at the speed of light. No pods at all are required. –  Dec 27 '17 at 15:51
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    If one can build a ship that can indeed travel close to speed of light, then the time dilation factor should make the hibernation pod not necessary. e.g. If a ship is travel at $0.9c$, the time dilation factor will be $\frac{1}{\sqrt{1-0.9^2}} \approx 2.294$ which means one only need $100/(0.9\times 2.294) \approx 48.4$ years (from the passenger viewpoint) to reach the habitat. If travel at $0.99c$, it will take $14.2$ year instead. – achille hui Dec 27 '17 at 15:55
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    Assume the ship start at zero velocity, accelerate at standard gravity $g \approx 9.8 {\rm ms^{-2}}$ until it has traveled for $50 {\rm ly}$ and then de-accelerate with $g$ again until it reach the habitat planet. If I didn't make any mistake, it will take $101.343$ year earth time for the ship to complete the journey. However, for the passengers onboard, only about $3.04$ year has passed! The whole deal is definitely a big Christmas present for the seller of hibernation pod (or whoever authorize to sign the contract ;-p) – achille hui Dec 27 '17 at 16:42

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I assume it is possible if one person sleeps for $40$ years and then the other sleeps for the remaining $40$ years. That way both live till $70$ and enjoy $10$ years of roaming about the planet, assuming that no one dies in between.

For the love of maths
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