John does half piece of work in 3 hours. Joe does ¼ of the remaining work in 1 hour and George finishes remaining work in 5 hours. How long would it have taken the three working together to do the work?

\(2\frac{8}{11}\)

Time taken by John to  do whole work = 6 hours

Time taken by Joe to do \(\frac{1}{8}\) part  of work is 1 hour

Time taken by Joe to do whole work = 8 hours

Remaining work = \(\frac{1}{2}\) - \(\frac{1}{8}\) = \(\frac{3}{8}\) part of work

Time taken by George to do \(\frac{3}{8}\) is 5 hours

Time taken by George to do whole work = \(\frac{40}{3}\) hours

Total work = Efficiency × Number of days

Time taken = \(\frac{120}{44}\) = 2\(\frac{8}{11}\) days