If I understand your question correctly, this should work:
int hours = 0;
Calendar calendar = Calendar.getInstance();
calendar.set( Calendar.HOUR_OF_DAY, hours );
this.startTime = calendar.getTime();
this.endTime = calendar.getTime();
If not, can you show us the full method in which you want to replace the date code?
EDIT: . , , Calendar, . , . , , calendar.getTime().
if (query.getCount() > 0 && query.moveToFirst())
{
int hours = 0;
int minutes = query.getInt( "startTimeOfDayMins" );
Calendar calendar = Calendar.getInstance();
calendar.set( Calendar.HOUR, hours );
calendar.set( Calendar.MINUTE, minutes );
this.startTime = calendar.getTime();
this.daysOfWeek = ( query.getString( "daysOfWeek" ) ).toLowerCase();
calendar.set( Calendar.MINUTE, minutes + query.getInt( "durationMins" ) );
this.endTime = calendar.getTime();
this.context = null;
}