Answer
The recession speed is $~~v = 0.8c$
Work Step by Step
We can use the relativistic Doppler equation to find the recession speed:
$\lambda = \lambda_0~\sqrt{\frac{1+\beta}{1-\beta}}$
$3\lambda_0 = \lambda_0~\sqrt{\frac{1+\beta}{1-\beta}}$
$3 = \sqrt{\frac{1+\beta}{1-\beta}}$
$9 = \frac{1+\beta}{1-\beta}$
$9~(1-\beta) = 1+\beta$
$10\beta = 8$
$\beta = 0.8$
The recession speed is $~~v = 0.8c$
