Special relativity help

So initially ignoring relativity, after 3 half lives the muons decay to an 1/8 of there original number. Calling there half life T, the distance they travel in this time by the very basic equation s=vt, is S = 3TV where v is the velocity there going (this is arbitrary).Now of course this isn't the case , since they are going so fast there entire reference frame has slowed down and hence there half life is actually relativistic call this t. therefore the actual distance s is given by the formula s=3tV. (From a stationary observers point of view) The final step is the the relationship between the two half lives t and T. Calling the gamma factor G, t=TG by standard results.
This means to obtain the gamma factor we have to divide the the relativistic half life by the normal half life. The final link of how this goes back to distances is the original equations. Rearranging for t and T: t = s/3V T=S/3V if we do t/T the 3V cancels out leaving us with s/S which is 4/1.5 giving us the answer.

I realise this is very wordy and possibly a bit confusing i can clarify!