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.