The New Horizons spacecraft passed Pluto in July 2015. At the time of closest approach on July 14, 2015, Pluto was 34 AU from the Earth. How long did it take for a radio signal (traveling at the speed of light) from New Horizons to travel from Pluto to the Earth at the time of closest approach?

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Despite using distances that are big, this question is using a basic equation.  Speed = Distance/Time.  That equation can be reordered to read Time = Distance/Speed.  

The distance in this case is 34 astronomical units.  I'll leave it in that unit.  Converting to miles or kilometers will make these numbers huge.  The speed of light is 300,000,000 m/s.  It is going to work best to convert the speed of light into astronomical units per second.  That number is 0.00200399 AU/sec.

We can now use the initial equation.  

Time = Distance/Speed

Time = 34 / 0.00200399

Time = 16966.1525257 seconds

Let's round that to 16,966 seconds.  Divide by 60 to get minutes.  

That's about 282.767 minutes.  Divide by 60 again to get hours.    

That's roughly 4.713 hours.

In hours, minutes, and seconds, that comes out to be 4 hours, 42 minutes, and 46 seconds.   

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