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Debt and Lines of Credit (Details)
3 Months Ended 6 Months Ended
Nov. 10, 2020
USD ($)
Jun. 29, 2018
USD ($)
Feb. 28, 2022
USD ($)
Feb. 28, 2021
USD ($)
Feb. 28, 2022
USD ($)
Feb. 28, 2021
USD ($)
Aug. 31, 2021
USD ($)
Interest Revenue (Expense), Net [Abstract]              
Interest expense     $ 6,400,000 $ 6,900,000 $ 12,600,000 $ 12,000,000.0  
Interest income     (400,000) (300,000) (700,000) (500,000)  
Interest expense, net     6,000,000.0 $ 6,600,000 11,900,000 $ 11,500,000  
Letters of Credit | New Revolving Credit Facility              
Line of Credit Facility [Abstract]              
Outstanding letters of credit     4,100,000   4,100,000    
Credit facility              
Line of Credit Facility [Abstract]              
Minimum interest coverage ratio   2.50          
Maximum leverage ratio   3.50          
Outstanding letters of credit     4,100,000   4,100,000    
Credit facility | Minimum              
Line of Credit Facility [Abstract]              
Facility fee (percent)   0.125%          
Credit facility | Maximum              
Line of Credit Facility [Abstract]              
Facility fee (percent)   0.25%          
Credit facility | New Revolving Credit Facility              
Line of Credit Facility [Abstract]              
Term of instrument   5 years          
Executed revolving credit facility   $ 400,000,000          
Borrowings outstanding under current Revolving Credit Facility     0   0   $ 0
Additional borrowing capacity under revolving credit facility     395,900,000   395,900,000    
Eurocurrency Rate | Credit facility | New Revolving Credit Facility | Minimum              
Line of Credit Facility [Abstract]              
Applicable margins based on company's leverage ratio, percentage   1.00%          
Eurocurrency Rate | Credit facility | New Revolving Credit Facility | Maximum              
Line of Credit Facility [Abstract]              
Applicable margins based on company's leverage ratio, percentage   1.375%          
Base rate | Credit facility | New Revolving Credit Facility | Minimum              
Line of Credit Facility [Abstract]              
Applicable margins based on company's leverage ratio, percentage   0.00%          
Base rate | Credit facility | New Revolving Credit Facility | Maximum              
Line of Credit Facility [Abstract]              
Applicable margins based on company's leverage ratio, percentage   0.375%          
ABL | Unsecured debt | 2.150% Senior Unsecured Notes Due December 2030              
Line of Credit Facility [Abstract]              
Aggregate principal amount $ 500,000,000            
Interest rate (percent) 2.15%            
Debt issuance price as a percentage of face value (percent) 99.737%            
Deferred issuance costs $ 4,800,000            
Term of instrument 10 years            
Debt outstanding     $ 494,700,000   $ 494,700,000