The water content in the boiler is 180 kg. The connected electric heater is 20 kW. Temperature of the water in starting is 27 Deg C. The final steam pressure required is 85 PSI.
First you have to heat the water and the boiler. Since you say nothing about the boiler you have to neglect the boiler part. You need to look up in a steam table the enthalpy of saturated liquid and vapor at 85 psi (99.7 psia, probably 100 psia is close enough) and figure out how much it changed. The part I don't know is how you know how much liquid you have and how much vapor you have without knowing the volume of the boiler. The two most plausible assumptions you can make here is that the boiler volume will only be large enough to hold the saturated liquid or that it will be so large as to require all the water to be vapor to be able to get to 85 psi. I would guess that you need to convert it all to steam so use that. So you compute the change in enthalpy from water to steam for the whole 180 kg and divide by the power input to get time to get there. Make sure to keep track of the unit conversions between metric and English units.
