A fisherman on a boat sailed against the current of the river, an empty flask fell from the boat into the river near the bridge. After that, having sailed $15$ minutes against the current of the river, the fisherman noticed his loss and swam in the opposite direction to catch up with the flask. What is the speed of the river if the fisherman caught up with the flask $4$ kilometres downstream of the bridge?
$v_1$ - current velocity
$v_2$ is the swimmer's speed
respectively $v_2-v_1$ is the upstream speed, $v_2 + v_1$ downstream after losing the flask, they moved away from each other at a speed $v_1 + v_2 - v_1$, which means in $15$ minutes we parted to $(v_1 + v_2 - v_1) * 15 = s$, $s$ is the final distance between them before the start of the convergence, then they began to converge $(v_2 + v_1 - v_1) * T = s$, $T$ is the approach time, we have
$v_2 * 15 = S$
$v_2 * T = S $
$T = 15$, from where we easily find $v_1 = 8$ km / h
right or wrong?