Answer
The recessional speed of the quasar as measured by astronomers in the other galaxy is $~~0.714~c$
Work Step by Step
Let $u'$ be the quasar's velocity relative to the Earth.
Let $v$ be the Earth's velocity relative to the galaxy.
Let $u$ be the quasar's velocity relative to the galaxy.
We can find $u$:
$u = \frac{u'+v}{1+\frac{u'v}{c^2}}$
$u = \frac{0.8c-0.2c}{1+\frac{(0.8c)(-0.2c)}{c^2}}$
$u = \frac{0.6c}{1-0.16}$
$u = 0.714~c$
The recessional speed of the quasar as measured by astronomers in the other galaxy is $~~0.714~c$
