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When working together, Arthur and Bea can complete a job in 4 hours.  Arthur and Chester can complete the same job in 5 hours.  Bea and Chester can complete the same job in 6 hours.  How will it take all 3 people working together?

 Sep 5, 2020
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1 /(a+b) = 4                 and        1/ (a+c)  = 5        and      1/(b+c) = 6

4a+4b=1                                         5a+5c=1                        6b + 6c =1

                                                  

a = 1/4-b                                    a = 1/5-c                  c = 1/6-b

 

        1/4-b  = 1/5 -c

         1/4-b  = 1/5 - 1/6+b

         1/4 -1/5+1/6 = 2b

             b = 13/120                  then   a =  17/120        and   c = 7/120

 

1/ ( 17/120 + 13/120 + 7/120) = x

x = 3.24 hours

                                                                      

                                                               

 

Is there a EASIER way to do this problem????  cheeky

 Sep 5, 2020

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