Answer
Please see the work below.
Work Step by Step
We know that
if $\mu_k=0$
then $a=gsin(\theta)=(9.8)sin28=4.60\frac{m}{s^2}$
Now $t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{(2)(100)}{4.60}}=6.593s$
If $\mu_k=0.17$
then $a=gsin(\theta)-\mu gsin(\theta)=(9.8)sin(28)-(0.17)(9.8)cos (28)=3.13\frac{m}{s^2}$
$t=\sqrt{\frac{2d}{a}}$
$t=\sqrt{\frac{2(100)}{3.13}}=7.994s$
Now we can find the difference as
$7.994-6.593=1.4s$
