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 , expressing both x and y as simplified fractions.

jxc516 Feb 26, 2021

#1**0 **

because Morgan can paint a room in 10 hours, she can paint 1/10 of a room in 1 hour, and sophia can paint 1/4 of a room in 1 hour, so 2(x/10+y/4)=y/10+x/4=1. simplifying, we get 4x+10y=2y+5x=20, and we can split that into 2x+5y=10 and 2y+5x=20. now we can just solve:

2x+5y=10

2y+5x=20

2y+4x/5=4

2y+5x=20

21x/5=16

x=$\boxed{\frac{80}{21}}$

160/21+5y=10

5y=50/21

y=$\boxed{\frac{10}{21}}$

SparklingWater2 Feb 27, 2021