Mike, Connor and Floyd can finish a certain piece of work in 8, 22 and 33 days, respectively. All three of them started the work together. Mike left the work after 4 days and Connor left just 2 days before the work was completed. Find the total number of days taken for the work to be completed.
7.8
Mike works 4 days at rate \(\tfrac18\), contributing \(4\times\tfrac18=\tfrac12\) of the work.
Let total days be T. Connor works \((T-2)\) days at rate \(\tfrac1{22}\), and Floyd works T days at rate \(\tfrac1{33}\).
Total work: \(\tfrac12 + \dfrac{T-2}{22} + \dfrac{T}{33} = 1\).
Multiplying through by 66: \(33 + 3(T-2) + 2T = 66 \Rightarrow 5T + 27 = 66 \Rightarrow T = 7.8\).
Hence, the total work takes 7.8 days to complete.
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