Triangle $RST$ is similar to triangle $UVW$, where $R,S$, and $T$ correspond to $U,V$, and $W$, respectively. The length of $\overline{RS}$ is 35 and the length of $\overline{ST}$ is 63. If the length of $\overline{UV}$ is 25, what is the length of $\overline{VW}$?