How can I show that the composition of two coverings is also a covering? I'm trying to prove the following:

Let $\varpi ' : X'' \to X'$ and $\varpi : X' \to X$ be two coverings
  and let $X$ be a locally simply connected space. Prove that $\varpi \circ \varpi ' : X'' \to X$ is also a covering.

I am completely stuck at this, I have no idea about how to use the locally simply connected hypotesis about $X$. How should I proceed?
Any hint would be greatly appreciated.

Firts assume that $X$ is simply connected. Then $X'= X\times D$, $D$ a space with the discrete topology. Therefore $X"= X\times D'\times D$ for another discrete space $D'$, and the result follows. The general case follows from the  hypothesis : let $x\in X$ and $U$ a simply connected neigbourhood of $X$, the previous argument applied to $U\subset X$ $\omega^{-1} U \subset X'$ and $\omega "^{-1}(U)\subset X"$ prove that the result.
