Answer
about 4.15 minutes
Work Step by Step
Evaluate the indefinite integral first,
$\displaystyle \int\frac{1}{T-100}dt=\left[\begin{array}{l}
u=T-100\\
du=dt
\end{array}\right]=\int\frac{du}{u}$
$=\ln|u|+C = \ln|T-100|+C$
$t=\displaystyle \frac{10}{\ln 2}\int_{250}^{300}\frac{1}{T-100}dt=\frac{10}{\ln 2}[\ln|T-100|]_{250}^{300}$
$=\displaystyle \frac{10}{\ln 2}(\ln 200-\ln 150)\approx$4.15037499279
... about 4.15 minutes
