Answer
$\frac{R_a}{R_f}\approx0.44$
$100$ weeks.
Work Step by Step
Step 1. Use $v=0.9c$ in the given formula $R_a=R_f\sqrt {1-0.9^2}\approx0.44R_f$. Thus we have the relative aging rate as $\frac{R_a}{R_f}\approx0.44$
Step 2. Let $R_a=44$ weeks, we have $R_f=\frac{44}{0.44}=100$ weeks. That is, 100 weeks have passed for your friend.
