A static load test has been conducted on a $60$ ft long, $16$ in square reinforced concrete pile which has been driven from a barge through $20$ ft of water, then $31$ ft into the underlying soil. Telltale rods A and B have been embedded at points $30$ ft and $59$ ft from the top of the pile, respectively. The data recorded at failure was as follows: Load at head $=139,220lb,$ settlement at head $=1\mathrm{.}211in,$ settlement of telltale rodA$=1\mathrm{.}166$ in$,$ settlement of telltale rod $B=1\mathrm{.}141$ in$.$ The side friction resistance between the head of the pile and point A is negligible. Determine: a$)$ equivalent modulus of the pile, $E$ using the data from telltale rod $A$;$b)$ the average $f_n$ and $q_n^{\text{'}}$ for the pile.