The total 'x' distance of the drive goes from x = 0 to x = 32 for 'x' distance 32
the part of the drive where you can hear the radio goes from x = 11.35 to 19.64 for x distance 8.29
percentage of distance you can hear the station is then 8.29/32 = 25.9%
You COULD find the distance between the starting and end points and then the points of intersection...BUT that is a much more difficult method than is necessary...
distance formula d^2 = (x1-x2)^2 + (y1-y2) ^2 (recognize this as modified pythagorean theorem) ..... so for the two intersection points you would have to calculate the 'y' coordinates (you have the x's)
for A to B d^2 = (0-32)^2 + ( 31-0)^2 resulting in d = 44.55 miles
I would use a quadratic formula calculator like this one:
https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php
