It takes 32 minutes for 3 people to paint 4 walls. How many minutes does it take 4 people to paint 7 walls?

Answer 1

This is a rate problem as it deals with three different units: minutes, people, and walls. We need to assume that all people are working at the same rate. To start to understand the problem, we first need to figure out how long it takes 1 person to paint 1 wall.

We can divide time (32 minutes) by # of walls (4 walls) to find out how long it would take for the total number of people to paint only 1 wall, in this case it would take 3 people a total of 8 minutes to paint one wall. To find out how long it would take one person to paint one wall we multiple 8 minutes by 3 as it would take three times as long with only one person. Therefore it takes one person 24 minutes to paint a wall.

Now lets apply this value of 24 minutes/wall for one person to the new data of 4 people and 7 walls. If there are 4 people, the work will be faster so we divide 24 by 4 which equals 6 minutes/wall. Then multiply by the number of walls which need to be painted (7 walls) by # of minutes/wall, 6 x 7 = 42 minutes which is our final answer.

Answer 2

1) 3 people do 4 walls in 32 minutes

We make the assumptions that all people work at the same rate and each person starts and finishes at the same time. Since there are 3 people, each person does 1/3 of the total work. Therefore each person finishes their portion of the job in 32 minutes

2) 3 * 1/3 = 1 person does 4 * 1/3 = 4/3 walls in 32 minutes

The unit rate (the rate for 1 person to do 1 wall) is as follows

3) 1 person does 4/3 * 3/4 = 1 wall in 32 * 3/4 = 24 minutes

Since we need 4 people to do 7 walls then 1 person needs to do 1/4 of the work. So the following is true

4) 4 * 1/4 = 1 person does 7 * 1/4 = 7/4 wall

As we said before in #3

1 person does 1 wall in 24 minutes

So we conclude

5) 1 person does 1 * 7/4 = 7/4 walls in 24 * 7/4 = 42 minutes

And finally

6) 1 * 4 = 4 people do 7/4 * 4 = 7 walls in 42 minutes