Let's say we are in a frame of reference S and we see a clock moving at velocity $c/2$. Let's say that a clock in our frame of reference reads $t=0$ when the moving clock reads $t'=0$. I want to then find out what time our clock will read when the moving clock reads $t=100$.
Here's what I did: We have $$t=\gamma\left(t'+\frac{vx'}{c^2} \right)$$ and we know that $t'=100$, $v=c/2$ and I suppose that $x'=vt'=ct'/2$ and so to give $$t=\gamma\left(t'+\frac{c^2t'}{4c^2} \right)=\frac{5}{4}\gamma t'$$ so here's the problem: shouldn't it be simply $$t=\gamma t'$$ what did I overlook? Thank you.
