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.

Guest Dec 27, 2020

#1**0 **

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.

Reflec Dec 27, 2020

#2**+1 **

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

CPhill Dec 27, 2020