allright where did I go wrong here....
Io = Vo/R = 6/16 = .375A
I1 = \(\frac{V1}{R+jwL}\) = \(\frac{5}{16+j(2pi60)(.025)}\) = \(\frac{5}{16 + j9.42}\) = .269@-30.48deg
I2 = \(\frac{V2}{R+jwL}\) = \(\frac{3}{16+j(6pi60)(.025)}\) = \(\frac{3}{16 + j28.27}\) = .092@-60.49deg
therefore
i(t) = .375 + .269cos(2pi60t - 30.48deg) + .092cos(6pi60t - 60.49deg)
P0 = 6*.375 = 2.25w
P1 = \(\frac{(5)(.269)}{.375}\)cos(30.48) = 3.09w
P2 = \(\frac{(3)(.092)}{.375}\)cos(60.49) = .363w
Ptotal = 2.25 + 3.09 + .363 = 5.7w