A set of chaining survey data is presented in Table $1$ below. Calculate the average distances of each line segment, corresponding discrepancy ratios, and the total distance of the entire route.

$($For distances, report to the nearest ${100}^{th}$ place, and for the discrepancy ratio, use only the whole number at the denominator. Failure following the reporting requirements will result in $5$ points deduction.$)$

$\backslash$table$[[$Line segments,FW Dist. $($ft$),$BW Dist. $($ft$),$Mean Dist. $($ft$),$Discrepancy Ratio$],[1-2,85\mathrm{.}03,85\mathrm{.}05,85\mathrm{.}04,\mathrm{.}02],[2-3,110\mathrm{.}65,110\mathrm{.}62,110\mathrm{.}64,-\mathrm{.}03],[3-4,102\mathrm{.}44,102\mathrm{.}47,102\mathrm{.}46,\mathrm{.}03],[4-5,98\mathrm{.}70,98\mathrm{.}71,98\mathrm{.}71,\mathrm{.}01],[5-6,107\mathrm{.}47,107\mathrm{.}5,107\mathrm{.}49,\mathrm{.}03],[$Sum$,504\mathrm{.}29,504\mathrm{.}35,504\mathrm{.}34,\mathrm{.}06]]$

Suppose that the chaining survey in problem $1$ was conducted on a hot day when the temperature of the chain was recorded as $100F$ using a $200-$footlong chain that is known to have a built$-$in error of $+0\mathrm{.}02$ per chain. Compute the length and temperature corrections for the chaining survey and report the corrected horizontal distance.