A truck travels $180$ km at $60$ km/h, then returns $180$ km at $45$ km/h. Which statement(s) correctly describe(s) the average speed for the entire round trip?\n\n(I) The average speed is exactly $52.5$ km/h\n(II) The average speed equals the harmonic mean of the two speeds\n(III) The average speed is less than the arithmetic mean of the two speeds