Question 6
The line $y = \tfrac{1}{3}x + 1$ divides the square region defined by $0 \le x \le 2$ and $0 \le y \le 2$ into an upper region and a lower region. The line $x = a$ divides the lower region into two regions of equal area. Then $a$ can be written as $\sqrt{s} - t,$ where $s$ and $t$ are positive integers. What is $s + t?$