A group of mountain climbers set up a camp at a $\pu{3 km}$ altitude and experience a barometric pressure of $\pu{0.69 atm}$. They discover that pure water boils at $\pu{90 ^\circ C}$ and that it takes $\pu{300 min}$ to make a "three-minute" egg. What is the ratio of rate constants at $\pu{100 ^\circ C}$ and at $\pu{90 ^\circ C}$ i.e. $\dfrac{k_\pu{100 ^\circ C}}{k_\pu{90 ^\circ C}}$?

How should I approach this problem? I have no idea what to do here, though it seems like an interesting problem. The given answer is

100