Ruan began painting a room at 9:00 AM. Leonardo, who can paint twice as fast as Ruan, started helping Ryan at 9:20 AM, and they worked together until the room was fully painted at 9:40am. What fraction of the room had been painted by 9:30 AM? Express your answer as a common fraction in lowest terms and clearly show/explain your reasoning.
+41 First set r to the speed Ryan paints the room.
So the equation is
40r+20(2r)=1
80r=1
This would work if the speed of paint the room was consent.
So
20r/80r=1/4
This is the amount of the room before Leonardo started helping.
Then 80r-20r=60r
60r/2=30r
30r/80r+1/4=3/8+1/4=3/8+2/8=5/8
So 5/8 of the room was painted by 9:30.
+129852 Call the part of room that Ryan can paint in the first 20 minutes, 1/x
When Leonardo joins in the part that is painted between 9:20 and 9:40 (20 minutes) is (1/x) + (2/x) = 3/x
So in 40 minutes the whole job is done....so
(1/x + 3/x) = 4/ (x) = 1 ⇒ x = 4
So....the part painted between 9 and 9:30 is
(1/4) + ( 1/2) (3/4) =
(1/4) + 3/8 =
2/8 + 3/8 =
5/8
