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
'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'