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**+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

CPhill
Oct 19, 2018

#2**+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

CPhill
Oct 19, 2018