We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
76
4
avatar+128 

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
avatar+19822 
+3

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
avatar+19822 
+1

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
avatar+128 
+1

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

 Sep 23, 2019
 #4
avatar+19822 
+1

You are welcome!   ~EP

ElectricPavlov  Sep 24, 2019

34 Online Users

avatar
avatar
avatar
avatar
avatar