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).

Guest Oct 28, 2019

#1**+1 **

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

ElectricPavlov Oct 28, 2019

#2**+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)

CPhill Oct 28, 2019