SOLUTION: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task i

Question 1208469: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

Answer by ikleyn(52765) (Show Source): You can put this solution on YOUR website!
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Working alone, A can complete a task in ‘a’ days and B in ‘b’ days.
They take turns in doing the task with each working 2 days at a time.
If A starts they finish the task in exactly 10 days.
If B starts, they take half a day more.
How long does it take to complete the task if they both work together?
~~~~~~~~~~~~~~~~~~~~~~

So, their rates of work are  1/a for A and 1/b for B.


In the first scenario, A works 6 days; B works 4 days.  So, first equation is

     +  = 1  (the entire job)         (1)


In the second scenario, A works 4.5 days; B works 6 days. So, second equation is 

     +  = 1  (the entire job)    (2)


To solve, multiply equation (1) by 3; multiply equation (2) by 2 and subtract the second from the first.


You will get then

     -  = 3 - 2,  or

     = 1.


Hence,  a = 9, which means that A makes the entire job in 9 days working alone.

Then from (1)

     = 1 -  = 1 -  = .


Hence, b = 12, which means that B makes the entire job in 12 days working alone.


Working together, they will complete the job in  

     =  = 5 days = 5 days.    ANSWER

Solved.

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