SOLUTION: If 3 people can paint 2 rooms in 4 days, how many people are needed to paint 12 rooms in 6 days?

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Question 1207697: If 3 people can paint 2 rooms in 4 days, how many people are needed to paint 12 rooms in 6 days?

Found 5 solutions by Edwin McCravy, josgarithmetic, greenestamps, mccravyedwin, ikleyn:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
If 3 people can paint 2 rooms in 4 days, how many people
are needed to paint 12 rooms in 6 days?
3 people can paint 2 rooms in 4 days, so 
3 people can paint 6 rooms in 12 days. Therefore,
6 people can paint 12 rooms in 12 days, so
12 people can paint 12 rooms in 6 days.

ANSWER: 12 people

You can also use the worker-time-job formula, which is:



where

W1 = the number of workers in the first situation.
T1 = the number of time units (days in this case) in the first situation.
J1 = the number of jobs in the first situation.

W2 = the number of workers in the second situation.
T2 = the number of time units (days in this case) in the second situation.
J2 = the number of jobs in the second situation.

W1 =  3             W2 = the unknown quantity     
T1 =  4             T2 = 6 
J1 =  2             J2 = 12







 reduces to  and  reduces to 



Multiply both sides by 2:

Answer = W2 = 12 workers.  (or 'people').

Edwin

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

Needed is for N workers each at rate then
for T time and W amount of work,
.

---
If 3 people can paint 2 rooms in 4 days,
---



---
how many people are needed to paint 12 rooms in 6 days?
---




Simple set of equations,


Divide the second equation by the first equation:



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


Another approach, which I personally find easiest and fastest....

Given: 3 people can paint 2 rooms in 4 days

New data: 12 rooms instead of 2
That's 6 times as many rooms; 6 times as many people are needed: 3*6 = 18 people

New data: 6 days instead of 4
That's 3/2 as many days; 2/3 as many people are needed: 18*(2/3) = 12

ANSWER: 12 people can paint 12 rooms in 6 days

Short solution, without all the words:
3*6*(2/3)=12


Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

I think the easiest way is to use the fact that 

 is always a constant.   

, so 6 is the constant.

So put x for the unknown, in this case the number of workers, 
and set it equal to the constant 6







Edwin

Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
If 3 people can paint 2 rooms in 4 days, how many people are needed to paint 12 rooms in 6 days?
~~~~~~~~~~~~~~~~~~~~~~

We want to solve the problem by writing a proportion.



    What quantity is the same to equate two sides of proportion ?

        - The rate of work is the same per day and per worker.



When 3 workers paint 2 rooms in 4 days, the rate of work is   =  = .


When x workers paint 12 rooms in 6 days, the rate of work is   = .


These two rates of work we want to equate (since they are equal)

     = .


From this proportion,  x = 2*6 = 12 workers.


ANSWER.  12 workers are needed.

Solved.

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

To see many other similar  (and different)  problems,  solved by the same method,  look into the lesson
    - Rate of work problems
in this site.

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



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