One system is comprised of a three phase heater (pure resistive). This heater is delta connected and has a power of 50,000W, at 60-Hz; a synchronous motor with a cylindrical rotor. This motor has fourth poles and is connected in a star, with a power of 30 hp at 60 Hz, this motor will be operating at 50% of its rated load and a torque angle of -16.4%, with an efficiency of 96% and synchronous reactance of 0.667 ohm / phase; This system also has an induction motor, 3, star (Y), works at 60-Hz and has 6 poles. This motor will be running at 75% of its rated load, but at an efficiency of 95.8% with a PF of 89.1%. For the entire system the voltage will be 460-V. Find:

a)the total real power of the system,

b)the synchronous motor power factor,

c)the powers, reactive and apparent as the system power factor,

d) draw the power diagram.