The work done by the motor to raise the boiler is equal to the increase in gravitational potential energy of the boiler, when raised from the floor to the platform at height h=15.0:
[tex]\Delta U = mg \Delta h=(175 kg)(9.81 m/s^2)(15.0 m)=2.58 \cdot 10^4 J[/tex]
This is equal to the work done by the motor, so it's equal to the energy it used. But the power is the energy per unit of time:
[tex]P= \frac{E}{t} [/tex]
And since the power of the motor is [tex]P=4.50 kW=4.5 \cdot 10^3 W[/tex], we can find the time needed to raise the boiler up to 15.0 m:
[tex]t= \frac{E}{P}= \frac{2.58 \cdot 10^4 J}{4.5 \cdot 10^3 W}=5.73 s [/tex]
