It takes 16 minutes for 9 people to paint 8 walls. How many minutes does it take 4 people to paint 6 walls? This is a ratio problem that I'm stuck on.

Question

This is a popular question on the internet, but I just cannot figure out how they got the answer:

It takes 16 minutes for 9 people to paint 8 walls. How many minutes does it take 4 people to paint 6 walls?

This is a ratio problem that I'm stuck on.

I know it will take 1/8 of the time to paint one wall. I don't understand how everyone figures out that for only one person, it will take 9 times as long.

Then they say it will take 2 x 9= 18 minutes for one person to paint one wall. I don't know where the 2 x 9 comes from?

In the end they say the number of minutes it will take for one person to paint 6 walls is 18 x 6 = 108
The number of minutes it will take for 4 people to paint 6 walls is 108 ÷ 4 = 27. The answer is 27, but what I need is a for dummies explanation on how it became 27. Thank you for your time!

Answer 1

"I don't understand how everyone figures out that for only one person, it will take 9 times as long." - Well if 9 people take a certain amount of time to paint a job, then one person would take nine times as long.

 

1/8 of 16 minutes is 2 minutes for 1 wall to be painted by the 9 people.

 

So, if 9 people can paint one wall in 2 minutes, and it takes 1 person 9 times as long, then it will take one person 9 x 2 = 18 minutes to paint one wall.

 

so, 1 person would take 18 minute /wall times 6 walls, and 18 x 6 = 108

 

with 4 people, the time is 108/4 = 27.

 

I hope that helped...

Answer 2

you may wish to consider this as a rate and time relationship

walls painted=painter rate∗time

painter rate =[(8 walls painted/9 painters)]/16 minutes

painter rate=8/144 walls painted per painter minute

let x=painter minutes

6 walls painted=(8/144 walls painted per painter minutes)∗x

solve for x

x=6/(8/144) painter minutes

x=108 painter minutes (to complete 6 walls)

108 painter minutes/4 painters=27 minutes to complete the painting of 4 walls

you will find that simple physics problems such as these are best solved when the unit rates are displayed in the problem solution