How long did radio commands take to travel from the Earth to Voyager as it passed Neptune?
Well, radio waves are electromagnetic waves, so they travel at the speed of light, which is about 3x108 m/s. According to https://www.physlink.com/reference/astrophysical.cfm , Neptune is 4.5x1012 m away from the sun, and since Earth is only 1.5x10^11 m away from the sun, I'll just assume that we're about 4.5x1012 m away from Neptune.
This means that the radio signals took (4.5x1012 m) / (3x108 m/s) = 15,000 seconds (or a little over 4 hours) to get to the Voyager.
Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN
'There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.'