Final answer:
Hubble's Law relates the recession speed of a galaxy to its distance using the Hubble constant. To find the time light takes to travel from a quasar, first find the distance using the recession speed and the Hubble constant, then divide by the speed of light.
Step-by-step explanation:
According to Hubble's Law, the speed of recession (v) of a galaxy is proportional to its distance (d) from us, given by the formula v = H0 x d, where H0 is the Hubble constant. To find the time taken by light to travel from a quasar to Earth, we first need to establish the distance to the quasar using the observed speed of recession and the Hubble constant. Once the distance is calculated, the time in years for light to cover that distance is simply the distance divided by the speed of light, considering that light travels roughly 9.46 trillion kilometers in one year.
For example, if a galaxy is observed to be moving away from us at 18,000 km/s, Hubble's Law indicates that the galaxy is d = v / H0 Mly away. Using an approximate value of the Hubble constant as 20 km/s/Mly, the distance would be 18,000 km/s divided by 20 km/s/Mly, which equals 900 Mly. Consequently, to convert this distance to the time required by light to travel, we simply need to state that time in years is equivalent to the distance in light-years, which would be 900 million years in this example.