Answer
$0.823\text{ hours}$
Work Step by Step
Substitute $T=100$ into the equation:
$$100=20+140e^{-0.68h}$$ $$80=140e^{-0.68h}$$ $$40=70e^{-0.68h}$$ $$\ln 40=\ln \left(70e^{-0.68h}\right)$$ $$\ln 40=\ln 70+\ln e^{-0.68h}$$ $$\ln 40=\ln 70-0.68h\ln e$$ $$\ln 40=\ln 70-0.68h$$ $$\ln 40-\ln 70=-0.68h$$ $$h=\frac{\ln 40-\ln 70}{-0.68}$$ $$h=0.823$$
Thus, it took about $0.823$ hours for the object to reach the temperature of $100^\circ$.
