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Revenue Recognition - Contracted Balances (Details) - USD ($)
$ in Millions
12 Months Ended
Oct. 02, 2020
Sep. 27, 2019
Cost of services provided    
Disaggregation of Revenue [Line Items]    
Capitalized contract cost, amortization $ 21.8 $ 20.0
Cost of services provided | Uniform    
Disaggregation of Revenue [Line Items]    
Capitalized contract cost, amortization 325.7 318.2
Cost of services provided | Operating Lease Right-of-Use Assets    
Disaggregation of Revenue [Line Items]    
Capitalized contract cost, amortization 23.1 16.0
Depreciation and amortization    
Disaggregation of Revenue [Line Items]    
Capitalized contract cost, amortization 20.8 20.5
Depreciation and amortization | Property, Plant and Equipment | Leasehold Improvements    
Disaggregation of Revenue [Line Items]    
Capitalized contract cost, amortization $ 160.8 $ 149.0