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Derivative Financial Instruments and Fair Value Measurements - Fair Value Measurements (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
	Jun. 30, 2024	Jun. 30, 2024	Sep. 30, 2023
Derivative financial instruments
Decrease in fair value	$ (1.6)
Interest Rate Swap and Interest Rate Cap \| Other current assets
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	15.3	$ 15.3	$ 17.2
Interest Rate Swap and Interest Rate Cap \| Other non-current assets
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	67.1	67.1	$ 37.5
Interest Rate Swap and Interest Rate Cap \| Other Noncurrent Liabilities
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	0.1	0.1
Level 1
Derivative financial instruments
Equity fair value	12.0	12.0
Level 3 \| Revolving credit facility
Derivative financial instruments
Revolving credit facility	$ 26.3	26.3
Designated as Hedging Instrument \| Cash Flow Hedging \| Interest Rate Swap
Derivative financial instruments
Losses recognized in income		$ 0.0