SOLUTION: Let's say you have 4 painters that have completed 12 rooms in 8 hours. Assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?

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Question 1199624: Let's say you have 4 painters that have completed 12 rooms in 8 hours. Assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?

Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let's say you have 4 painters that have completed 12 rooms in 8 hours.
Assuming they are working at the same efficiency, how many hours does it take
7 painters to paint 21 rooms?
~~~~~~~~~~~~~~~ 

Let the number of hours in the second scenario be h.


The rate of job of each painter in the 1st scenario is  12%2F%284%2A8%29 = 3%2F8  of the room per hour.


The rate of work of each worker in the 2nd scenario is  21%2F%287%2Ah%29 = 3%2Fh.


The rate of work is the same in both scenario, so we can write this equation

    3%2Fh = 3%2F8.


It implies h = 8 hours.    ANSWER

Solved.

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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28NUMBERofWORKERS%29%28WORKRATE%29%28TIME%29=AMOUNTofWORK

4 painters that have completed 12 rooms in 8 hours.
4%2Ar%2A8=12

how many hours does it take 7 painters to paint 21 rooms?
x, number of asked hours of time
7rx=21


Divide entire second equation by entire first equation, and solve for x.
The number r will simply not be needed (cancels in the operation).

%287rx%29%2F%284%2A8%2Ar%29=21%2F12
%287%2F%284%2A8%29%29x=%287%2A3%29%2F%284%2A3%29
x=%284%2A8%2A7%2A3%29%2F%284%2A3%2A7%29
highlight%28x=8%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You have received two responses showing very different ways to solve the problem using formal algebraic methods.

Here is a quick and easy informal method for solving the problem.

From the first scenario to the second, the number of painters increases by a factor of 7/4. Increasing the number of painters decreases the required time, so the 8 hours in the first scenario gets multiplied by 4/7 because of the increased number of workers.

From the first scenario to the second, the number of rooms to be painted increases by a factor of 21/12 = 7/4. Increasing the number of rooms increases the required time, so the 8 hours in the first scenario gets multiplied by 7/4 because of the increased number of rooms.

Combining the effects of the increased number of workers and the increased number of rooms, the 8 hours in the first scenario gets multiplied by (4/7)(7/4) = 1 -- so the time required for the second scenario is the same 8 hours.

That's a lot of words to explain a simple method for solving the problem. Without all the words, the complete path to the solution is this:

(8)*(4/7)*(7/4) = 8

ANSWER: 8 hours