I'm trying to understand the solution to the first of the challenge problems in the Units and Dimensional analysis unit of the introduction to mechanics.

The solution is here - I'm looking at problem 1:
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf

I can follow the assumptions right up to the part where they take t is approximately A1 / A2 and from this they say therefore Y=1 Z=-1 ... I don't see how you can make this deduction. Are we plugging it in somewhere?

Question

I'm trying to understand the solution to the first of the challenge problems in the Units and Dimensional analysis unit of the introduction to mechanics.

The solution is here - I'm looking at problem 1:
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/introduction-to-mechanics/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf

I can follow the assumptions right up to the part where they take t is approximately A1 / A2 and from this they say therefore Y=1 Z=-1 ... I don't see how you can make this deduction.  Are we plugging it in somewhere?