COMBINED WORK, AND MIXTURE WORD PROBLEMS COLLEGE ALGEBRA 2

Mixture and Combined work problems involves using a scenario to create an algebraic equation in one variable and then solving it algebraically. The most difficult part of Mixture and combined work word problems is setting up the algebraic equation. Multiple methods can be used to set up the equation ranging from chart method, formulaic method to bucket method. A formula is almost always necessary to create an equation. In our video tutorials below we use the bucket method to set up the relationship between parts of the problem.  .The bucket method can be used to solve combined work and mixture problems.  The most important thing to determine is the quantity that is being added. 

Example 1
Working together,  Esteban and Ray-J can clean up a room in 8 hours. If Esteban were working alone it will take him 5 hours to complete the task. How long will it take Ray-J to clean up the room by himself?

Estebans rate  + Ray-J's rate=  Combined rate      
           
                    1/8   +   1/x             =            1/5
Find the lcd of the fractions on the left side

                   x/8x +  8/8x         = 1/5
                    (x+8)/8x=1/5
                    cross multiply
                  5(x+8)=8x(1)
                    5x+40=8x
                     3x=   40
                       x=40/3=13 hrs 20 minutes

It will take Ray J 13 hours and 20 minutes to clean the room if he is working alone.

2.2 Combined Work Word Problems College Practice Worksheet Doc Algebra 2