Question 1197111
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abbie paints twice as fast as beth and three times as fast as cathie. 
if it takes them 60 minutes to paint a living room with all three working together,
how long would it take each woman working alone?
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<pre>
Their rates of work are in proportion A : B : C = 6 : 3 : 2.

So, let 2x be the Cathie's rate of work; 3x be Beth's rate of work and 6x be Abbie's rate of work.


According to the condition, 

    6x  + 3x + 2x = {{{1/60}}}  of the job

         11x      = {{{1/60}}}

           x      = {{{1/660}}}.


So, Abbie's rate of work is   {{{6/660}}} = {{{1/110}}}  of the job per minute;

    Beth's  rate of work is   {{{3/660}}} = {{{1/220}}}  of the job per minute;

    Cathie  rate of work is   {{{2/660}}} = {{{1/330}}}  of the job per minute.


It means that Abbie  needs 110 minutes = 1 hour and 50 minutes to complete the job alone;

              Beth   needs 220 minutes = 3 hour and 40 minutes to complete the job alone;

              Cathie needs 330 minutes = 5 hour and 30 minutes to complete the job alone.
</pre>

Solved.


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As this problem is twisted, it shows me that it is slightly higher that the average school level (with a claim).


Therefore, my response is written in an adequate style, without chewing.