$(20$ points$)$ A constant head permeability test was performed on a layered soil with a cross$-$sectional area of $5m^2.$ If the hydraulic conductivity of soil $A$ is $1*{10}^{-3}\frac{m}{s}.$ and a flowrate in the test of $q=0\mathrm{.}0125\frac{m^3}{s}$ was measured, determine the hydraulic conductivity and head loss in soil B$.$ Head loss CANNOT be neglected in either soil.