Problem $5$: Do Problem $3-18(15$ pts$)$

The existing posted speed limit on a section of highway is $55m\frac{i}{h}$ and studies have

shown that that the current $85$ th percentile speed is $65m\frac{i}{h}.$ If the posted speed limit is to

be increased to the current $85$ th percentile speed, what should be the increase in the radius

of a curve that is just adequate for the existing posted speed limit$?$

Assume a superelevation rate of $0\mathrm{.}08$ for the existing curve and for the redesigned curve.