28 men are needed to paint the room in 3 hours
Given that it takes 12 hours for 7 men to paint a room
We are asked to find number of men required to paint the room in 3 hours
Recognize, "paint the room" is 1 task. One job.
7 men -------- 12 hours ------ 1 job
(7/7) = 1 men ------- 12 x 7 (84) ------- same 1 job
The one men is rate is 84 hours to do the job
We can express this as 1/84 jobs per hour, the one-person rate
Now lets find how many men needed to paint the room in 3 hours
Let the required number of men for 3 hours be "a"
The rates of each person is simply additive.
[tex]a \times \frac{1}{84} \times 3 = 1[/tex]
corresponds to rate x hours = jobs and "a" is a variable for how many men
[tex]a \times \frac{1}{28} = 28[/tex]
Thus 28 men are needed to paint the room in 3 hours
