Q: A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 3.0 m/s at the end of 3.0 s. At that instant, the kinetic energy of the system is 60 J and each mass has moved a distance of 4.5 m. Determine the values of m1 and m2.
A:

Where Et = Energy total
ps* We cleaned up the problem a little bit (it took a few pages to answer the question), so this is the nitty gritty of the question, two equations with two unknowns.