Hi guys thanks for the help, here is the problem.

Morgan can paint a room in 10 hours, while Sophia can paint it in 4 hours. If Morgan paints for x hours and Sophia paints for y hours, they will finish half of the painting, while if Morgan paints for y hours and Sophia paints for x hours they will paint the whole room. Find the ordered pair (x,y), expressing both x and y as simplified fractions.

EvanWei123 Sep 22, 2019

#1**0 **

Painting the room = 1 whole job

Morgan rate = 1/10

Sophia rate = 1/4

Rate x time = 1 job

1/10 x + 1/4 y = 1/2 and

1/10 y + 1/4 x = 1 solve for x,y

Multiply top equation by - 2.5

(-2.5)/10 x - (2.5/4) y = -1.25

-1/4 x - 5/8 y = -1 .25

and add to the second equation to get

1/10 y - 5/8 y = -.25 solve for y

4/40 y - 25/40 y = -.25

-21/40 y = - .25

y = 10/21 hr Substitute this into one of the origianl equations to find 'x'

1/10 (10/21) + 1/4 x = 1

1/21 + 1/4 x = 1

1/4 x = 20/21

x = 80/21 x,y = ( 3 17/21 , 10/21)

ElectricPavlov Sep 22, 2019

#2**0 **

Here is agraphical solution (I used to check my answer above):

https://www.desmos.com/calculator/gdlnsk708d

ElectricPavlov Sep 22, 2019