$[ A ]_{0} e ^{-\left( in ^{2} / 300\right)^{t}}=4[ B ]_{0} e ^{(-\ln 2 / 180) t }$

$e^{\left(\frac{in^{2}}{180}-\frac{in^{2}}{300}\right)}=4$

$\left(\frac{\ln ^{2}}{180}-\frac{\ln ^{2}}{300}\right) t =\ln 4$

$\left(\frac{1}{180}-\frac{1}{300}\right) t=2 \Rightarrow t=\frac{2 \times 180 \times 300}{120}=900 sec$