$3\mathrm{.}10$ An equal$-$tangent vertical curve was designed in

$2012($to $2011$ AASHTO guidelines$)$ for a design speed

of $70m\frac{i}{h}$ to connect grades $G_1=+1\mathrm{.}2\%$ and $G_2=$

$-2\mathrm{.}1\%.$ The curve is to be redesigned for a $70-m\frac{i}{h}$

design speed in the year $2025.$ Vehicle braking

technology has advanced so that the recommended

design deceleration rate is $25\%$ greater than the $2011$

value used to develop Table $3\mathrm{.}1,$ but due to the higher

percentage of older persons in the driving population,

design reaction times have increased by $20\%.$ Also,

vehicles have become smaller so that the driver's eye

height is assumed to be $3\mathrm{.}0ft$ above the pavement and

roadway objects are assumed to be $1\mathrm{.}0ft$ above the

pavement surface. Compute the difference in design

curve lengths for the $2012$ and $2025$ designs.