Answer
(a) The galaxy is moving away from us at a speed of 14,500 km/s.
(b) The galaxy is $6.9\times 10^8~ly$ from the Earth.
Work Step by Step
(a) $\frac{\lambda_o-\lambda_r}{\lambda_r} = \frac{v}{c}$
$v = (\frac{\lambda_o-\lambda_r}{\lambda_r} )~c$
$v = (\frac{455~nm-434~nm}{434~nm} )~(3\times 10^5~km/s)$
$v = 14,500~km/s$
The galaxy is moving away from us at a speed of 14,500 km/s.
(b) $d = \frac{v}{H_0} = \frac{14,500~km/s}{(21~km/s)/10^6~ly} = 6.9\times 10^8~ly$
The galaxy is $6.9\times 10^8~ly$ from the Earth.
