It takes 12 hours for 7 men to paint a room.How many men would be needed to paint the room in 3 hours?

28 men are needed to paint the room in 3 hoursSolution:Given that it takes 12 hours for 7 men to paint a roomWe are asked to find number of men required to paint the room in 3 hoursRecognize, "paint the room" is 1 task. One job.7 men -------- 12 hours ------ 1 job(7/7) = 1 men ------- 12 x 7 (84)  ------- same 1 jobThe one men is rate is 84 hours to do the jobWe can express this as 1/84 jobs per hour, the one-person rateNow lets find how many men needed to paint the room in 3 hoursLet 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