Income Taxes - Rate (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation at federal statutory income tax rate, amount	$ 46.3	$ 30.6	$ 25.9
Income tax expense attributable to NCI	0.0	(7.6)	(19.5)
State income taxes, net of effect on federal tax	8.4	4.7	4.0
Transaction costs	0.0	2.0	0.0
Other, net (none in excess of 5% of computed tax)	0.2	(0.1)	(1.6)
Income tax expense, total	$ 54.9	$ 29.6	$ 8.8