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Long-Term Debt (Details) - USD ($)
 3 Months Ended 9 Months Ended
Mar. 10, 2022
Oct. 21, 2019
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Sep. 30, 2022
Debt Instrument              
Long-term and short-term debt, combined amount     $ 919,000,000.0   $ 919,000,000.0   $ 939,000,000.0
Unamortized Debt Issuance Expense     (8,500,000)   (8,500,000)   (9,500,000)
Long-term debt     910,500,000   910,500,000   929,500,000
Payments of debt issuance, extinguishment costs and deferred financing fees         0 $ 11,900,000  
Loss on extinguishment of debt, net     0 $ 0 0 17,600,000  
7.00% Senior Notes Maturing in March 2030              
Debt Instrument              
Long-term debt, gross $ 840,000,000.0   840,000,000.0   840,000,000.0   840,000,000.0
Payments of debt issuance, extinguishment costs and deferred financing fees 10,200,000            
Revolving Credit Facility              
Debt Instrument              
Long-term debt, gross     79,000,000.0   79,000,000.0   99,000,000.0
Maximum borrowing capacity on line of credit 250,000,000.0            
Deferred financing fees 1,500,000            
Proceeds from borrowing under line of credit         115,000,000.0 109,000,000.0  
Repayments of lines of credit         135,000,000.0 25,000,000.0  
Remaining borrowing capacity on line of credit     171,000,000.0   171,000,000.0   151,000,000.0
Letters of credit outstanding, amount     $ 0   $ 0   $ 0
Letter of Credit              
Debt Instrument              
Maximum borrowing capacity on line of credit $ 20,000,000.0            
Old Revolving Credit Facility [Domain]              
Debt Instrument              
Maximum borrowing capacity on line of credit   $ 200,000,000.0          
Proceeds from borrowing under line of credit           0  
Repayments of lines of credit           0  
Term Loan              
Debt Instrument              
Long-term debt, gross   700,000,000.0          
Repayments of Debt           519,800,000  
Write-off of Unamortized Debt Discount           6,900,000  
Write-off of Interest Rate Swap Loss in AOCI           6,100,000  
Write off of Deferred Debt Issuance Cost           4,600,000  
Periodic payment of long-term debt principal   8,750,000          
Excess cash flow prepayment           $ 81,400,000  
Letter of Credit - Old Credit Agreement              
Debt Instrument              
Maximum borrowing capacity on line of credit   $ 20,000,000.0