Can Momentum Save an Astronaut 200m Away from the ISS?

[MathewsMD]

An 80 kg astronaut has become detached from the safety line connecting her to the International Space Station. She's 200m from the station, at rest relative to it, and has 4 min of air remaining. To get herself back, she tosses a 10 kg tool kit away from the station at 8 m/s. Will she make it back in time?

In the question, the solution uses momentum and calculates it for both the astronaut and tool box since they are at rest only relative to the space station, not the rest frame. Here it shows initial momentum is equal to 0, though. If they are calculating momentum in the rest frame, shouldn't there be an initial momentum of p = (m_a + m_t)v_rel, but it is 0...why? Is not the astronaut and toolbox in motion initially and once again afterwards? Any explanation on why the momentum is paired the way it is would be very helpful! :)

 

[mic*]

What is the rest frame, if it is not a frame of reference where the object/s of interest are at rest?

No other relative position or motion information has been given in this problem, other than " She's 200m from the station, at rest relative to it".

Following from this, the formula you have stated for initial momentum is correct - p = (ma + mt)vrel.
Now what value would you choose for vrel?