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.
First set r to the speed Ryan paints the room.
So the equation is
This would work if the speed of paint the room was consent.
This is the amount of the room before Leonardo started helping.
So 5/8 of the room was painted by 9:30.
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 =