Quotient Space of $\mathbb{R} \times [0,1] $

Question

The Quotient space of $X=\mathbb{R}\times [0,1] $ is defined by the equivalence relation $(x,t) \sim(x+1,t)$, $x\in\mathbb{R}$ and $t \in [0,1]$.

I need to prove that the space $X/\sim$ is a Hausdorff and compact space.