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# help with algebra

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A carpenter is working on a deck.  He hires two assistants who work 60% as fast as he works.  If all three work together on the deck, they should finish in what fraction of the time that he would take working alone?

Jan 11, 2021

#1
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Call the  number  of  hours it takes the  carpenter to finish  the  job =  x

So......the fraction of the  job that he can finish   in   one hour is  1/x

So.....the fraction of the  job that  of the other two can do in one  hour   = .60 (1/x)

So....the total   fraction of work  done in one hour  by all three working together is

1/ x  +  .60 (1/x)  +  .60 (1/x)   =      (1 + .60 + .60) / x  =   (2.2) / x

So....the total time they take is the reciprocal of this  =   x / (2.2)

So....the fration of the time that they would  take  working together compared to  the carpenter working alone  is

( x/ 2.2)   / x   =

(x /2.2) * (1/x)  =   1 / 2.2   =  10/22 =   5/11  of the time   Jan 11, 2021
#2
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1 / (1+.6+.6) = .4545         46/100th of the time     or     45.5 % of the original time

Jan 11, 2021
#3
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1 / (1 + .6 + .6) = 1/2.2 = 5/11

Guest Jan 11, 2021