SOLUTION: John can do a piece of work in 15 days. John and David can do the same amount work in 6 days. In how many days David alone can do the same amount of work?

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Question 633499: John can do a piece of work in 15 days. John and David can do the same amount work in 6 days. In how many days David alone can do the same amount of work?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
John can do a piece of work in 15 days. John and David can do the same amount work in 6 days. In how many days David alone can do the same amount of work?
There are two ways to do the problem: (1) in your head and (2) by algebra.

The first way is "in your head":

The LCM of 6 days and 15 days is 30 days.  So in 30 days John could do 2 pieces
of work. And if they worked together for 30 days they could do 5 pieces of
work.  So if they worked together for 30 days, John would do 2 pieces of work
and therefore David would do the other 3 pieces of work.  Therefore David can
do 3 pieces of work in 30 days, so he can do 1 piece of work in 10 days.

The second way is "by algebra":

Make this chart:

            jobs done          time in days       rate in jobs/day
John
David
together

John can do 1 job in 15 days, so we fill in 1 for his jobs done and 15
for his time in days:

            jobs done          time in days       rate in jobs/day
John            1                   15                    
David
together

John and David together can do 1 job in 6 days, so we fill in 1 for his jobs
done and 6 for their time in days:

            jobs done          time in days       rate in jobs/day
John            1                   15                    
David
together        1                    6                  

Let x = the number of days it would take David alone to do one piece of
work. So we fill in 1 for David's jobs done and x for his time in days:

            jobs done          time in days       rate in jobs/day
John            1                   15                    
David           1                    x
together        1                    6 

Next we fill in the three rates in jobs/day by putting jobs over days:

            jobs done          time in days       rate in jobs/day
John            1                   15                 1/15                    
David           1                    x                  1/x
together        1                    6                  1/6

             
        The equation comes from the sum of their rates equals their
combined rate:

                 %28matrix%284%2C1%2C%0D%0A%0D%0A%22John%27s%22%2Crate%2Cin%2C%22jobs%2Fday%22%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A%22David%27s%22%2Crate%2Cin%2C%22jobs%2Fday%22%29%29 = 

                 1%2F15 + 1%2Fx = 1%2F6

Get an LCD of 30x and multiply through and the answer will be x=10 days,
the same answer as when we do it in our head.

Edwin