Question

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

Answer 1

so we have 3 folks painting 4 walls, now each one of them works for 32 minutes

person 1............. 32 mins

person 2............. 32 mins

person 3............. 32 mins

for a total of 32+32+32 = 96 minutes worth of work. That's for 4 walls, how many minutes worth is just 1 wall?

96 ÷ 4 = 24 mins.

so to paint a wall, it takes 24 mins of work worth.

so then, to paint 7 walls, that'd be 7 * 24 = 168 minutes worth of work.

what about for 4 folks doing it? How many times does 4 go into 168? 168 ÷ 4 = 42 mins.

Answer 2

42 minutes

Explanation:

Work is often measured in units of persons times time. Here, we need to find the amount of work per wall. That is ...

work per wall = (32 min)(3 people)/(4 wall) = 24 people·min/wall

If we let x represent the number of minutes required by 4 people to paint 7 walls, and we assume the same amount of work is required for each wall, we have ...

(x min)(4 people)/(7 wall) = 24 people·min/wall

Multiplying by 7 wall and dividing by 4 people, we have ...

x min = (24 people·min/wall)(7 wall)/(4 people) = 42 min

It will take 4 people 42 minutes to paint 7 walls.

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Another way to consider this is to realize that there are 7/4 times as many walls and 4/3 as many people. The time will be proportional to the number of walls and inversely proportional to the number of people. (The inverse of 4/3 is 3/4.) So, the time for the second job is ...

(32 min)(7/4)(3/4) = 32(21/16) min = 42 min