To solve the astronaut's problem it is necessary to quickly consider the conservation of the moment.
By definition we know that,
Initial Momentum = Final Momentum
Where,
Human mass
Tank mass
v is the initial and final velocity of each object
In the case of the initial part we know that it is in a state without movement with respect to the ship.
In the case of the final moment there is a speed injection thanks to the oxygen tank, then,
Re-arrange to find the final velocity for astronaut,
Replacing
The astronaut has 4 minutes of air and must travel 200 meters therefore,
Re-arrange to find the time,
<em>He/She will reach the spacecraft within the stipulated time</em>