Official solution
\[{{dp} \over {dt}} = {{p - 900} \over 2}\]
\[\int\limits_{850}^0 {{{dp} \over {p - 900}} = \int\limits_0^t {{{dt} \over 2}} } \]
\[ \Rightarrow \] \[\ln |p - 900|_{850}^0 = {t \over 2}\]
\[ \Rightarrow \] \[\ln 900 - \ln 50 = {t \over 2}\]
\[ \Rightarrow \] \[{t \over 2} = \ln 18\]
\[ \Rightarrow t = 2\ln 18\]