According to Fick's Law of diffusion, the rate of gas exchange across an alveolar membrane, $R$, can be modeled by the formula:

$R=\frac{k\cdot A\cdot \Delta C}{d}$

where $k$ is a constant, $A$ is the total surface area of the alveoli, $\Delta C$ is the concentration gradient, and $d$ is the thickness of the alveolar wall.

A disease causes chronic inflammation of the lungs. This results in the total surface area of the alveoli, $A$, being reduced to $60\%$ of its original value, and the thickness of the alveolar wall, $d$, being increased by a factor of $1.5$.

Assuming $k$ and $\Delta C$ remain constant, determine the ratio of the new rate of gas exchange to the original rate.