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28 men are needed to paint the room in 3 hours
<h3><u>Solution:</u></h3>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.
corresponds to rate x hours = jobs and "a" is a variable for how many men
Thus 28 men are needed to paint the room in 3 hours
what we can do is hmmmm get the LCD of all fractions, and multiply both sides by that LCD, let's see, we have denominators of 2, 3 and 12, so we can use the LCD of 12, and multiply both sides by 12 to do away with the denominators.