  We consider, in the continuous time version, $\gamma$ independent random
walks on $\mathbb{Z_+}$ in random environment in the Sinai's regime. Let
$T_\gam$ be the first meeting time of one pair of the $\gamma$ random walks
starting at different positions. We first show that the tail of the quenched
distribution of $T_\gamma$, after a suitable rescaling, converges in
probability, to some functional of the Brownian motion. Then we compute the law
of this functional. Eventually, we obtain results about the moments of this
meeting time. Being $\Eo$ the quenched expectation, we show that, for almost
all environments $\omega$, $\Eo[T_\gamma^{c}]$ is finite for
$c<\gamma(\gamma-1)/2$ and infinite for $c>\gamma(\gamma-1)/2$.
