The shifted Lonely Runner Conjecture

Given pairwise distinct positive velocities $v_1,\dotsc,v_n \in \mathbb{R}$ and arbitrary starting points $s_1,\dotsc,s_n \in \mathbb{R}$, the distance from $s_j+tv_j$ to the nearest integer should be at least $\frac{1}{n+1}$ simultaneously for some real number $t$ and every $1\leq j\leq n$. Shifted Lonely Runner Conjecture. There is a real number $t$ such that, for all $1\leq j\leq n$, the distance of $s_j+tv_j$ to the nearest integer is at least $\frac{1}{n+1}$. This is the shifted variant of the Lonely Runner Conjecture, allowing arbitrary individual starting points rather than a common starting point. The source gives no resolution status for this variant.