John ,Rick , and Molli are painting a room together. It takes all of them 16 hours to paint the room to perfection. It takes Joh
n 8 hours to paint the room alone , and it takes Rick 2 hours to paint the room alone. What is the hourly rate it take’s of john to paint the room alone?
John's hourly rate is 1/8 of the room per hour. Rick's hourly rate is 1/2 of the room per hour. Molli's hourly rate would be 3/8 of the room per hour.
It takes Molli 2 2/3 hours to paint the room alone.
Explanation Since John paints the entire room (100%=1) in 8 hours, he would paint 1/8 of the room in 1 hour. Since Rick paints the entire room (100%=1) in 2 hours, he would paint 1/2 of it in 2 hour.
We do not yet know Molli's rate, so we will call it x.
We know that 1/8+1/2+x = 1 hour.
We will use 8 as a common denominator: 1/8+4/8+8x/8 = 1
Adding the numerators, (1+4+8x)/8 = 1
Multiply both sides by 8: 1+4+8x = 8
Add like terms: 5+8x = 8
Subtract 5 from both sides: 5+8x-5=8-5 8x=3
Divide both sides by 8: 8x/8 = 3/8 x = 3/8
Molli's rate is 3/8.
Since she can paint 3/8 of the room in 1 hour, we can set up the equation 3/8x = 1
Divide both sides by 3/8: 3/8x ÷ 3/8 = 1 ÷ 3/8 x = 1/1 ÷ 3/8 = 1/1 × 8/3 = 8/3 x = 2 2/3
This is the amount of time it takes Molli to paint the entire room.
