Acquisitions and Dispositions - Schedule of Aggregate Cash Consideration and Total Assets Acquired and Liabilities Assumed (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Business Acquisition [Line Items]
Inventories	$ 0.2	$ 0.4	$ 0.0
Other current assets	0.0	0.0	0.2
Property, plant and equipment	5.0	6.4	10.0
Operating lease assets	23.2	9.7	9.6
Goodwill	44.3	29.0	39.1
Other current liabilities	(0.1)	(0.7)	(0.8)
Operating lease liabilities	(23.2)	(9.1)	(8.9)
Other noncurrent liabilities	(3.0)	(3.7)	(1.7)
Total net assets acquired	53.3	36.3	50.7
Non-cash consideration	(0.6)	0.0	0.0
Total cash consideration transferred	$ 52.7	$ 36.3	$ 50.7
Weighted average useful life	7 years	9 years	9 years
Capital Lease Obligations
Business Acquisition [Line Items]
Business combination recognized identifiable liabilities assumed, finance lease obligation, current	$ 0.1	$ 0.2	$ 0.1
Business combination, recognized identifiable asset acquired and liability assumed, lease obligation	3.0	3.7	1.7
Assets held under capital and finance leases
Business Acquisition [Line Items]
Business combination, recognized identifiable assets acquired assumed, finance lease asset	3.1	3.8	1.8
Reacquired franchise rights
Business Acquisition [Line Items]
Intangible assets	$ 6.4	$ 4.0	$ 2.8
Weighted average useful life	7 years	9 years	10 years
Gain (loss) on contract termination	$ 0.0
Other intangible assets
Business Acquisition [Line Items]
Intangible assets	$ 0.5	$ 0.3	$ 0.4