In hydrogen spectrum the wavelength of ${\mathrm{H}}_{\alpha }$ line is $656 \mathrm{nm},$ whereas in the spectrum of a distant galaxy, the H$\alpha$ line wavelength is measured to be equal to $706 \mathrm{nm}.$ The speed of the galaxy with respect to the earth is estimated to be 

If a star, emitting light of frequency v, goes away from the earth with a speed $v,$ the apparent frequency $v\text{'}$ as observed on earth is

$v^{\mathrm{\prime }}=v\left(\frac{c}{c+v}\right)$

where $c=$speed of light. Since  $v=\frac{c}{\lambda }\text{ and }{v}^{\mathrm{\prime }}=\frac{c}{{\lambda }^{\mathrm{\prime }}},$

$\begin{array}{l}\frac{c}{{\lambda }^{\mathrm{\prime }}}=\frac{c}{\lambda }\left(\frac{c}{c+\mathrm{v}}\right)\\ \Rightarrow \mathrm{v}=\frac{c}{\lambda }\left({\lambda }^{\mathrm{\prime }}-\lambda \right)\\ =\frac{3\times {10}^8}{656}\times (706-656)\\ =2\times {10}^7{\mathrm{ms}}^{-1}\end{array}$