Income Taxes - Components of Income Before Income Taxes and Reconciliation of Statutory Federal Income Tax (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Income before income taxes
United States	$ 242.7	$ 119.1	$ 250.8
Non-U.S.	(6.2)	25.0	9.2
Total income before income taxes	$ 236.5	$ 144.1	$ 260.0
U.S. statutory tax rate	21.00%	21.00%	21.00%
Income taxes computed at U.S. statutory tax rate	$ 49.7	$ 30.3	$ 54.6
(Decrease) increase in amount computed resulting from:
Unrecognized tax benefits	0.1	0.1	0.8
State taxes, net of federal benefit	11.2	5.2	9.3
International rate differential	0.1	(0.4)	0.0
Permanent items	0.1	(1.0)	0.5
Remeasurement of net deferred taxes	(1.1)	(0.5)	0.1
Return-to-provision adjustments	(0.9)	(0.4)	0.6
Change in valuation allowances	(27.7)	1.8	0.0
Tax Matters Agreement activity	5.4	0.0	(5.6)
Other	0.2	(0.4)	(0.4)
Income tax expense	$ 37.1	$ 34.7	$ 59.9
Effective tax rate	15.70%	24.10%	23.00%