Question 1184062
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Ron and Sam take 1 hour to paint 7/12 of the living room. 
Sam and Tom take 1 hour to paint 8/15 of the living room. 
Ron and Tom take 1 hour to paint 9/20 of the living room. 
How long will it take for Ron, Sam and Rom to paint the living room together?
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Let r be the Ron's rate of work (in parts of the living room per hour);

    s be the Sam's rate of work,  and

    t be the Tom's rate of work.


From the condition, we have  


    r + s = 7/12     (1)

    s + t = 8/15     (2)

    r + t = 9/20     (3)


Add the equations (1), (2) and (3). You will get

    
    2(r + s + t) = {{{7/12 + 8/15 + 9/20}}} = {{{35/60 + 32/60 + 27/60}}} = 94/60.

Hence,

     r + s + t = 47/60.


It means that Ron, Sam and Tom will complete painting the room in  {{{60/47}}} hours = 1 {{{13/47}}} hours.    <U>ANSWER</U>
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Solved.