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

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

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