Earth's moon is an average of 2.39 x 10^5 miles away. On average, how many seconds would it take for light to travel from Earth to the moon?

Question

How can I solve this using dimensional analysis?

Answer 1

We know we need the answer in seconds. We need the conversion factor for the speed of light is miles per second which is approximately 186000 miles per second or 186000 miles / 1 second.

As we want the answer in seconds, we write the conversion factor so that seconds is in the numerator

1 second / 186000 miles. If we multiply this factor by the distance to the moon, we get

1 second / 186000 miles x 2.39 x 10^5 miles = 1.28 seconds. Note that that the unit miles is both in the numerator and denominator and therefore cancel out leaving only seconds as the unit.