SOLUTION: a girl can build a project on 12 days. a boy can build the same project in 8 days. if they worked together on this project how long will it take them to finish the project?

Question 473321: a girl can build a project on 12 days. a boy can build the same project in 8 days. if they worked together on this project how long will it take them to finish the project?
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
a girl can build a project on 12 days. a boy can build the same project in 8 days. if they worked together on this project how long will it take them to finish the project?

Make this chart:

                     number      
                       of       time        rate
                    projects     in          in
                      done     hours    projects/hour
Girl
Boy
Girl & Boy together

Let the answer by x hours for both of them working together
to do 1 project. So we put x for the hours working together.

Since the girl can do 1 project in 12 hours, we put 1 for the
number of projects and 12 for the number of hours.

Since the boy can do 1 project in 8 hours, we put 1 for the
number of projects and 8 for the number of hours.

                     number      
                       of       time        rate
                    projects     in          in
                      done     hours    projects/hour
Girl                    1       12 
Boy                     1        8
Girl & Boy together     1        x

Next we fill in the rates in projects/hour by dividing
number of projects by hours:

                     number      
                       of       time        rate
                    projects     in          in
                      done     hours    projects/hour
Girl                    1       12          1/12
Boy                     1        8           1/8
Girl & Boy together     1        x           1/x

The equation comes from:

                 

  
                          

Multiply through by 24x

                 2x + 3x = 24

                      5x = 24

                       x = 

                       x = 4.8 hours or 4 hours 48 minutes. 

Edwin

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