Question 1169052
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Tom and dick working together can perform a task in 2 hours and 24 minutes. 
Dick and harry working together can perform the same task in 3 hours and 36 minutes. 
If dick works alone, he can complete the task in 6 hours. 
How long will it take tom and harry perform the task working together ?
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<pre>
Let T be the rate of Tom  (i.e. the part of the job he makes in each hour).

Let D be the rate of work for Dick, and

let H be the rate of work for Harry.


Then we have these two equations

    T + D = {{{1/((12/5))}}} = {{{5/12}}}    (1)   (here  {{{12/5}}}  represents  2 {{{2/5}}} hours = 2 hours and 24 minutes)

    H + D = {{{1/((18/5))}}} = {{{5/18}}}    (2)   (here  {{{18/5}}}  represents  3 {{{3/5}}} hours = 3 hours and 36 minutes)


Adding these equations, you get

   T + H + 2D = {{{5/12}}} + {{{5/18}}} = {{{15/36}}} + {{{10/36}}} = {{{25/36}}}.    (3)


We also know that the rate of work for Dick is  {{{1/6}}}  of the job per hour.


Hence, from (3) we have

    T + H + {{{2/6}}} = {{{25/36}}},  or

    T + H = {{{25/36}}} - {{{2/6}}} = {{{25/36}}} - {{{12/36}}} = {{{13/36}}}.


It means that Tom and Harry will complete the job in {{{36/13}}} hours = 2 {{{10/13}}} hours = 2 hours 46 minutes and 9 seconds (rounded).    <U>ANSWER</U>
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Solved.