John does $\frac{1}{2}$ piece of work in 3 hours, Joe does $\frac{1}{4}$ 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?

Given:

John does $\frac{1}{2}$ piece of work in 3 hours

Joe does $\frac{1}{4}$ of the remaining work in 1 hour and

George finishes remaining work in 5 hours

To do: Find how long would it take three of them if they work together

Solution:

John does $\frac{1}{2}$ piece of work in 3 hours or in 1 hour John does $\frac{1}{6}$work

Remaining work = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

Joe $\frac{1}{6}$ (remaining work) =$\frac{1}{4}\times$ $\frac{1}{2}$ = $\frac{1}{8}$ in 1 hour

Remaining work = $\frac{1}{2}$ - $\frac{1}{8}$ = $\frac{4-1}{8} = \frac{3}{8}$

George does $\frac{3}{8}$ work in 5 hours or $\frac{3}{40}$ work in 1 hour

So in 1 hour all three work to finish $\frac{1}{6} + \frac{1}{8} + \frac{3}{40}$

                                                                =$\frac{ 20}{120} + \frac{15}{120} + \frac{9}{120}$

                                                                =$\frac{ 44}{120}$

                                                                 = $\frac{11}{30}$ work

So all three can together finish work in $\frac{30}{11} = 2 \frac{ 8}{11}$ hours

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Updated on: 10-Oct-2022

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