The Rank of an Endomorphism over a Quotient space, which is generated by an invariant subspace

Question

I have problems answering the second part of the following question:

Let $U$ be a $K$-vectorspace with finite dimension, $W \subset U$ a subset of $U$ and $\varphi :U\to U$ an endomorphism.

1.) Show: $W$ is $\varphi$-invariant $\Leftrightarrow$ $\overline{\varphi}:U/W\to U/W$ is welldefined
2.) Determine the rank of $\overline{\varphi}$ in dependence of rank $\varphi$ and rank $\varphi_{|W}$

Thank you, for taking the time to help me with my question.