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Revenue Recognition - Disaggregated revenues (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Revenue Recognition      
Total revenue $ 13,340.9 $ 13,240.0 $ 13,642.5
Cost reimbursable      
Revenue Recognition      
Total revenue 5,319.4 5,734.5 5,958.2
Guaranteed maximum price      
Revenue Recognition      
Total revenue 4,582.7 3,896.8 3,962.6
Fixed price      
Revenue Recognition      
Total revenue 3,438.8 3,608.7 3,721.7
Americas      
Revenue Recognition      
Total revenue 10,228.3 10,138.3 10,390.8
Europe, Middle East, Africa      
Revenue Recognition      
Total revenue 1,588.1 1,620.3 1,752.1
Asia Pacific      
Revenue Recognition      
Total revenue $ 1,524.5 $ 1,481.4 $ 1,499.6