SOLUTION: please help me solve this problem, it takes 16 minutes for 9 people to paint 8 walls. how many minutes does it take for 4 people to paint 6 walls?

Question 1062099: please help me solve this problem,
it takes 16 minutes for 9 people to paint 8 walls. how many minutes does it take for 4 people to paint 6 walls?
Found 3 solutions by josgarithmetic, stanbon, math_helper:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
, Work Rate Rule, T time, R work rate, w amount of work.

If n is how many workers each working at rate R, then rate for this group working together is nR.

Let t be how many minutes, unknown, for the group of the 4 workers:

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
it takes 16 minutes for 9 people to paint 8 walls. how many minutes does it take for 4 people to paint 6 walls?
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time is directly related to number of walls and indirectly
related to number of people doing the job.
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t = k*w/p
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Solve for "k" using "16 min for 9 people to paint 8 walls"::
16 = k*8/9
k = 18
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Equation:
t = 18*w/p
---
Solve:: minutes for 4 people to paint 6 walls ?
t = 18*6/4
time = 27 minutes
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Cheers,
Stan H.
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

We first need to find the work-per-person (sometimes this type of thing is called "normalization"), once we know that, its easy to mix and match number of people and number of walls.
�
The 9 people paint 8/16 = 1/2 wall every minute
Each person does 1/9 of that: Work_per_person = (1/2)*(1/9) = 1/18 wall/minute
�
4 people paint 6 walls: (6 walls/4 persons) / (1/18 ) wall/minute/person
= 6*18/4 minutes
= 27 minutes.
�
Another, more direct, way to do this:
16 minutes * 9 people/4 people * 6 walls/8 walls = 27 minutes
I just set each fraction according to the qualitative nature of the 2nd configuration, with respect to "will it take longer or shorter?" That decides how to set the numerator and denominator.
I specified the units because they help prevent forgetting something.
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