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Rowena can paint a room in 14 hours, while Ruby can paint it in 6 hours. If Rowena paints for x hours and Ruby paints for y hours, they will finish half of the painting, while if Rowena paints for y hours and Ruby paints for x hours they will paint the whole room. Find the ordered pair (x, y).

 Oct 28, 2019
 #1
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Here is a very similar question ....can you see the method to solve this problem?

 

https://web2.0calc.com/questions/a-challenging-rate-problem-please-help-asap#r1

 Oct 28, 2019
 #2
avatar+106539 
+1

Each hour, Rowena paints  1/14  of the room

And each hour, Ruby paints 1/6 of  the room

 

 

So.....we have that

 

(1/14)(x)  + ( 1/6)(y)  = 1/2

(1/14)(y)  + (1/6)(x)  =  1   

 

(1/14)x  + (1/6)y  =  1/2

(1/6)x + (1/14)y  =  1  

 

Multiply both equations through by  42

 

3x  + 7y   =  21     ⇒   21x + 49y  =  147       (1)

7x +  3y  =   42     ⇒   -21x -  9y  =  -126       (2)

 

Add (1)  and (2)  and we have that

 

40y  = 21

y = 21/40

 

And 

3x + 7(21/40)  = 21

3x  + 147/40  = 21

3x  =  21  - 147/40

3x  =  693/40

x = (693/3)/40  =  231/40

 

So  (x, y)  =  (231/40, 21/40)

 

 

cool cool cool

 Oct 28, 2019

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