$[70$ points$]$ Three wells $(A,B,$ and $C)$ are installed in an aquifer. $B$ is $10km$ east of point $A,$ and $C$ is $10km$ north of point $A.$ The water level at $B$ is $50cm$ below $A,$ and the water level at $C$ is $70cm$ below $A.$ It is estimated that the hydraulic conductivity along line $AB$ is $10\frac{m}{d}$ with a porosity of $0\mathrm{.}2,$ and along line $AC$ is $5\frac{m}{d}$ with a porosity of $0\mathrm{.}1.$ Please:

$(1)$ Calculate the hydraulic gradients along lines $AB$ and $AC,$respectively.

$(2)$ Calculate the specific discharges along lines $AB$ and $AC,$ respectively.

$(3)$ Calculate the actual velocities along lines $AB$ and $AC,$ respectively.

$(4)$ Assume there is a contamination at well A$,$ calculate the how long it will take for

contamination to transport from $A$ to $B$ and from $A$ to $C,$ respectively.