Question

John ,Rick , and Molli are painting a room together. It takes all of them 16 hours to paint the room to perfection. It takes John 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?

Answer 1

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.

Step-by-step 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.