Upon the written petition or request of at least one third of the resident electors and a like proportion of the resident freeholders of the age of twenty-one years being filed with the county board of education, asking for the same and stating the rate of tax levy proposed, which shall not exceed fifteen mills, the county board of education shall order the board of trustees of such school district to hold an election at some place within the district, after giving notice of the time and place thereof for at least two weeks in some newspaper published within the county and by posting notice thereof in at least three public places within such school district for such length of time, unless there be no newspaper published within the county, in which event the posting of the notices as above shall suffice.