Q$1(30$ pts$).$ A sag type parabolic vertical curve was designed according to rider's comfort criteria; using the following formula to calculate the length of the vertical curve:

$L=A.\frac{V^2}{395}(in$ meters$)$

If the mid$-$curve offset distance for this curve is $1\mathrm{.}36$ m $,$ find:

a$)$ design speed of the highway if $G_1=-2\mathrm{.}4\%$ and $G_2=4\mathrm{.}4\%$

b$)$ the offset distances for every $20$ m starting from PVC$.$