> Let's consider a different problem: Let u = the rate at which I
> spend my money. Let v = the rate at which I earn money. Let L = the
> amount of money I have in the bank. How long will it take before my
> bank account is empty?
>
> I would set up the equation as
>
>     ut = vt + L
>
> and solve for t. You say I'm doing a Galilean transform? Whose
> frame of reference am I transforming to?

From the ground frame in which two distances and one
velocity is used to the moving frame in which one distance and
two velocities are used. Time is invariant, so you are allowed
to use t in either frame.
Androcles