Emergency in space

You have been hired to check the technical correctness of a TV show where a space shuttle astronaut becomes stranded during a space walk. The astronaut’s safety line has broken, and her thruster pack has been damaged and no longer works. She is approximately 200 m from the shuttle and drifting away from it at about 1.5 m/s. She estimates that she only has about 10 minutes of air remaining. To get back to the shuttle, she decides to unstrap her 10-kg tool kit and throw it away with all her strength, so that it has a speed of 7 m/s. Her mass, including the space suit, is 80 kg. In the script, she survives, but is this reasonable? Since none of the data values given in this problem are exact (they all are reported to only one significant digit), which ones are most critical in determining the fate of this astronaut?