Why Radio waves are electromagnetic waves, so in free space they travel at the speed of light, about 300,000,000 meters per second (3 x 10^8 m/s, often written as c). This is the number that makes the wavelength formula work: wavelength in meters equals 300 divided by the frequency in MHz. Nothing about the transmitter power or frequency changes this speed.
Watch out The choices given in miles per hour are the wrong units entirely; light does about 186,000 miles per second, not 300 million miles per hour. Half that value, 150,000,000, is not a physical constant here.
3 x 10^8 meters per second: three zeros short of a billion, and always meters, never miles.