during how much of the drive will you pick up a signal from the transmitter?

Question

A small radio transmitter broadcasts in a 54 mile radius. If you drive along a straight line from a city 65 miles north of the transmitter to a second city 64 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

x² + y² = 54² Circumference of radio signal.

y = (-65x / 64) + 65 Equation of drive path

Determine common solution (two points) and calculate the distance between them.