Income Taxes - Components of Net Deferred Tax Asset and Liability Accounts (Details) - USD ($) $ in Millions	Sep. 30, 2023	Sep. 30, 2022
Deferred tax assets:
Self-insurance reserves	$ 31.8	$ 30.7
Deferred compensation	2.8	3.0
Payroll related accruals	22.8	19.7
Other accrued expenses	0.0	5.4
Allowance for doubtful accounts	1.3	1.0
Lease liabilities	23.6	22.6
Net operating loss carryforward	7.1	8.5
Business interest expense	10.4	0.0
Other non-current deferred tax assets	4.5	3.3
Total non-current deferred tax assets	104.3	94.2
Valuation allowance	(5.1)	0.0
Total deferred tax assets	99.2	94.2
Deferred tax liabilities:
Intangible assets	46.2	47.0
Property and equipment	57.3	78.5
Deferred revenue	15.0	10.6
Prepaid assets	0.2	0.2
Lease assets	22.0	20.9
Other non-current deferred tax liabilities	6.0	0.2
Total non-current deferred tax liabilities	146.7	157.4
Total net deferred tax liabilities	47.5	63.2
Classification on balance sheets:
Other assets	3.6	5.4
Deferred tax liabilities	$ 51.1	$ 68.6