The power in a 3 - (ϕ)

Given:

$W_1+W_2=50\ kW..................(1)\\ $

$pf=0.6\ (lagging)$

$\phi=cos^{-1}(0.6)=53.13^{\circ}\\ tan\phi =\sqrt 3\dfrac{W_1-W_2}{W_1+W_2}\\ tan(53.13^{\circ})=\sqrt3\dfrac{W_1-W_2}{50}\\ W_1-W_2=38.49\ kW............................(2)$

Solving equations (1) and (2), 

$W_1=44.25\ kW; \ \ \ \ \ W_2=5.75\ kW$