Actually Mark, your comparison, using your own data, should look like this:
6 hrs x $15 = $2.50  3 kids = $0.83 per kid x 24 kids = $20.00/hr x 1440 hrs (8 hrs/day x 180 days) = $28,800/yr
or
6 hrs x $20 = $3.33  3 kids = $1.11 per kid x 24 kids = $26.66/hr x 1440 hrs (8 hrs/day x 180 days) = $38,400/yr
