Question 986933
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Since the machine  A  working alone can complete a job in  {{{3}}}{{{1/2}}}  hours,  it makes the part of  {{{1}}}:{{{3}}}{{{1/2}}} = {{{1}}}:{{{7/2}}} = {{{2/7}}}  of the entire work per hour. 

(It is rate of work for the machine  A). 


Since the machine  B  working alone can do the same job in  {{{4}}}{{{2/3}}}  hours,  it makes the part of  {{{1}}}:{{{4}}}{{{2/3}}} = {{{1}}}:{{{14/3}}} = {{{3/14}}}  of the entire work per hour. 

(It is rate of work for the machine  B).


Based on this data,  we can conclude that the machines  A  and  B  working together do  {{{2/7}}} + {{{3/14}}} = {{{4/14}}} + {{{3/14}}} = {{{7/14}}} = {{{1/2}}}  of the entire work in one hour. 


Hence,  it will take  2  hours for two machines to complete the job working together.


<B>Answer</B>. &nbsp;2 hours.


<B>PS</B>. &nbsp;It is the standard rate-of-work problem on joint work.

You can find numerous examples of such problems in the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using fractions to solve word problems on joint work</A>&nbsp; in this site.