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?

Algebra.Com
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)   (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   =   of the room per hour.


The rate of work of each worker in the 2nd scenario is   = .


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

     = .


It implies h = 8 hours.    ANSWER

Solved.

--------------

If you want to see many other similar solved problems,  look into the lesson
    - Rate of work problems
in this site.

It was written specially for you, to make your horizon WIDER.



Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!


4 painters that have completed 12 rooms in 8 hours.


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



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





Answer by greenestamps(13200)   (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
RELATED QUESTIONS

Three painters, Beth, Bill, and Edie working together can paint a home in 10 hours. Bill... (answered by lwsshak3)
6 painters paint 4 walls in 2 hours. How long time does it take for 4 painters to paint 8 (answered by richwmiller)
It takes 16 painters 7 hours to paint a building, how many painters working at the same... (answered by ewatrrr)
Ten painters working 8 hours daily take 15 days to paint 3 houses of 4 rooms each.How... (answered by ikleyn)
Jackie has completed 7 problems and is working at a rate of 4 problems per hour. Brandon... (answered by jorel555)
Each of two road graders can smooth a section of road in 10 hours working alone. After... (answered by mananth)
A Painting job can be completed in 12 hours by 3 professional painters. The same job can... (answered by josmiceli)
Ten Painter Working 8 Hours Daily take 15 Days To paint 3 Houses Of 4 Rooms Each. How... (answered by ankor@dixie-net.com)
If 2 painters can paint 2 rooms in 2 hours, how many painters are needed to paint 12... (answered by Alan3354)