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avatar+181 

1.) It takes max three times as long as Felix to complete the same job. When the men work together, they can complete the job in 9 hours. how many hours are required for max to do the job alone?

 

2.) Solve the equation [x] / [x-2] = [4] / [x^2-8x+12]  - [1] / [x-6]

which statements are true of the solutions(s) to the equation? 

Select each correct answer:

 

a.) there are two accecptable soutions to the equation.

 

b.) There are no accecptable solutions to the equation.

 

c.) 6 is an extraneous solution because it creates a 0 in the denominator

 

d.) there is one acceptable solution to the equation

 

e.) 2 is an extraneous solution because it creates a 0 in the denominator.

whosmans  Oct 19, 2018
 #1
avatar+90968 
+1

1.) It takes max three times as long as Felix to complete the same job. When the men work together, they can complete the job in 9 hours. how many hours are required for max to do the job alone?

 

Let  the portion of the job that Felix can complete in one hour  =  1/x

Let the portion of the job that Max can complete in one hour  =  1 / [3x]

 

So.....  rate * time  =  potion of job done....so

 

Portion that Felix can do in 9 hours  + portion that Max can do in 9 hrs  =  1 job done

 

(1/x) (9)  +  ( 1 / [3x] )  (9)  =  1

 

9/x  +  3/x  =  1

 

12/x  =  1

 

x = 12  means that Felix can complete the whole job in 12 hours working alone

 

So..Max can complete the job  in 3(12)  =  36 hours working alone

 

 

cool cool cool

CPhill  Oct 19, 2018
 #2
avatar+90968 
+1

2.) Solve the equation [x] / [x-2] = [4] / [x^2-8x+12]  - [1] / [x-6]

 

x / [ x - 2]   = 4 / [ ( x -6 ) ( x - 2) ]  - 1/ (x - 6)

 

Multiply through by  (x - 6) ( x - 2)

 

 

x ( x - 6)   =  4  - ( x - 2 )   simpify

 

x^2 - 6x  = 4 - x + 2

 

x^2 - 6x = 6 - x

 

x^2 - 5x - 6  =  0     factor

 

( x - 6) ( x + 1)  =  0      set both factors to 0   and solve for x and we have that

 

x = 6     or  x  =  -1

 

The first solution  makes a denominator  =  0....so it is extraneous

 

So.....

 

c.) 6 is an extraneous solution because it creates a 0 in the denominator

 

d.) there is one acceptable solution to the equation

 

 

cool cool cool

CPhill  Oct 19, 2018

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