Question 883377
two men A and B can finish a work in 16 days and 12 days respectively.A and B are working together after 4 days A left the work,then the remaining work completed by B in how many days?
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>>A...can finish a work in 16 days<<
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So A's rate is {{{matrix(1,2,1,job)/matrix(1,2,16,days)}}}{{{""=""}}}{{{matrix(1,2,1/16,job/(day))}}}
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>>...B can finish a work in...12 days<<
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So B's rate is {{{matrix(1,2,1,job)/matrix(1,2,12,days)}}}{{{""=""}}}{{{matrix(1,2,1/12,job/(day))}}}
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A and B are working together...(for)...4 days
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{{{(matrix(3,1,"A's",work, rate))}}}{{{""+""}}}{{{(matrix(3,1,"B's",work,rate))}}} {{{""=""}}} {{{(matrix(4,1,their,combined,work, rate))}}}

So their combined work rate is  

{{{matrix(1,2,1/16,job/(day))}}}{{{""+""}}}{{{matrix(1,2,1/12,job/(day))}}}{{{""=""}}}{{{matrix(1,2,1/16+1/12,job/(day))}}}{{{""=""}}}{{{matrix(1,2,3/48+4/48,job/(day))}}}{{{""=""}}}{{{matrix(1,2,7/48,job/(day))}}}

For those 4 days before A left, they had done

{{{matrix(1,2,7/48,job/(day))}}}{{{"×"}}}{{{matrix(1,2,4,days)}}} {{{""=""}}}{{{matrix(1,8,    7/48,"×",4,""="",7/12,of,the,job)}}}

So, when A left, there was still {{{5/12}}} of the job left for B to do by
himself. Suppose it took B alone N days to do the remaining {{{5/12}}} of the
job. Since B's work rate is {{{matrix(1,2,1/12,job/(day))}}}, the equation is:

{{{matrix(1,2,1/12,job/(day))}}}{{{"×"}}}{{{matrix(1,2,N,days)}}} {{{""=""}}}{{{matrix(1,4,5/12,of,the,job)}}}

or

{{{expr(1/12)N}}}{{{""=""}}}{{{5/12}}}

Multiply both sides by LCD=12

N = 5 days.

Edwin</pre>