SOLUTION: 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 d

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 d      Log On


   

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?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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?


>>A...can finish a work in 16 days<<


So A's rate is matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C16%2Cdays%29%22%22=%22%22matrix%281%2C2%2C1%2F16%2Cjob%2F%28day%29%29



>>...B can finish a work in...12 days<<


So B's rate is matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C12%2Cdays%29%22%22=%22%22matrix%281%2C2%2C1%2F12%2Cjob%2F%28day%29%29



A and B are working together...(for)...4 days


%28matrix%283%2C1%2C%22A%27s%22%2Cwork%2C+rate%29%29%22%22%2B%22%22%28matrix%283%2C1%2C%22B%27s%22%2Cwork%2Crate%29%29 %22%22=%22%22 %28matrix%284%2C1%2Ctheir%2Ccombined%2Cwork%2C+rate%29%29

So their combined work rate is  

matrix%281%2C2%2C1%2F16%2Cjob%2F%28day%29%29%22%22%2B%22%22matrix%281%2C2%2C1%2F12%2Cjob%2F%28day%29%29%22%22=%22%22matrix%281%2C2%2C1%2F16%2B1%2F12%2Cjob%2F%28day%29%29%22%22=%22%22matrix%281%2C2%2C3%2F48%2B4%2F48%2Cjob%2F%28day%29%29%22%22=%22%22matrix%281%2C2%2C7%2F48%2Cjob%2F%28day%29%29

For those 4 days before A left, they had done

matrix%281%2C2%2C7%2F48%2Cjob%2F%28day%29%29%22%D7%22matrix%281%2C2%2C4%2Cdays%29 %22%22=%22%22matrix%281%2C8%2C++++7%2F48%2C%22%D7%22%2C4%2C%22%22=%22%22%2C7%2F12%2Cof%2Cthe%2Cjob%29

So, when A left, there was still 5%2F12 of the job left for B to do by
himself. Suppose it took B alone N days to do the remaining 5%2F12 of the
job. Since B's work rate is matrix%281%2C2%2C1%2F12%2Cjob%2F%28day%29%29, the equation is:

matrix%281%2C2%2C1%2F12%2Cjob%2F%28day%29%29%22%D7%22matrix%281%2C2%2CN%2Cdays%29 %22%22=%22%22matrix%281%2C4%2C5%2F12%2Cof%2Cthe%2Cjob%29

or

expr%281%2F12%29N%22%22=%22%225%2F12

Multiply both sides by LCD=12

N = 5 days.

Edwin