SOLUTION: A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the entire work ?

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Question 699941: A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the entire work ?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Make this chart
                     No of jobs
                         or
                      fraction      Time in       Rate in  
                       of job        days         job/day 
A working alone
B working alone
A&B working together

>>...A can do 1/3 of a work in 5 days...<<
Fill that in:
                     No of jobs
                         or
                      fraction      Time in       Rate in  
                       of job        days         job/day 
A working alone          1/3          5
B working alone
A&B working together

B can do 2/5 of the work in 10 days. 
Fill that in:

                     No of jobs
                         or
                      fraction      Time in       Rate in  
                       of job        days         job/day
A working alone          1/3          5
B working alone          2/5         10 
A&B working together

In how many days both A and B together can do the entire work ?
Fill in unknown x for the time in days for A&B working together,
and fill in 1 for the number of jobs.

 
                     No of jobs
                         or
                      fraction      Time in       Rate in  
                       of job        days         job/day
A working alone          1/3          5
B working alone          2/5         10 
A&B working together      1           x

Next we fill in the Rate in jobs/day by dividing jobs by days:

                     No of jobs
                         or
                      fraction      Time in       Rate in  
                       of job        days         job/day
A working alone          1/3          5           (1/3)÷5 =(1/3)·(1/5)=1/15
B working alone          2/5         10           (2/5)÷10 = (2/5)·(1/10)=2/50=1/25  
A&B working together      1           x           1/x

                   The equation comes from %28matrix%284%2C1%2C%0D%0A%0D%0A%22A%27s%22%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A%22B%27s%22%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29 = %28matrix%285%2C1%2C%0D%0A%0D%0ATheir%2C+combined%2C+rate%2C+in%2C+%22job%2Fdays%22%29%29

                                     1%2F15 + 1%2F25 = 1%2Fx

Multiply through by LCD = 75 and solve.  You'll get x = 9%263%2F8 days.

Edwin