A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance

Question

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes $8	ext{ min and } 20	ext{ s}$ to cover this distance?

Professor PC Thomas Classes · Answer

Time $t = 8	ext{ min } 20	ext{ s} = 8 	imes 60 + 20 = 500	ext{ s}$. Speed $c = 1	ext{ new unit / s}$. Distance $= c 	imes t = 1 	imes 500 = 500	ext{ new units}$.