Calculus In Parabola

Calculus Level 5

Let $S$ be the focus of $y^2 = 4x.$ Point $P$ is moving on this curve such that its abscissa is increasing at a rate of $4$ units per second. Then the rate of increase of the length of projection of $SP$ on $x + y =1$ when $P$ is at $(4,4)$ is $\gamma$ .

Find $10^3\gamma$ to 1 decimal place.