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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.

Sep 22, 2019

#1
+21827
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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)

Sep 22, 2019
edited by ElectricPavlov  Sep 22, 2019
#2
+21827
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Here is agraphical solution (I used to check my answer above):

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

Sep 22, 2019
edited by ElectricPavlov  Sep 22, 2019
#3
+139
+1

Thank you ElectricPavlav that was alot of help Keep it up!

Sep 23, 2019
#4
+21827
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You are welcome!   ~EP

ElectricPavlov  Sep 24, 2019