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.
RELATED QUESTIONS