Answer
a) $v=0.66c$
b) $\Delta t_E=6.52 years$
Work Step by Step
a) $v=\frac{\Delta x_s}{\Delta t_s}=\frac{\Delta x_E\sqrt{1-\frac{v^2}{c^2}}}{\Delta t_s}=c\sqrt{1-\frac{v^2}{c^2}}=\frac{c}{\sqrt{1+\frac{(c\Delta t_S)^2}{(\Delta x_E)^2}}}=\frac{2.998\times10^8\frac{m}{s}}{\sqrt{1+\frac{(4.9ly)^2}{(4.3ly)^2}}}=0.66c$
b) $\Delta t_E=\frac{\Delta t_s}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{4.9 years}{\sqrt{1-\frac{(0.66c)^2}{c^2}}}=6.52 years$