Question

It takes 12 hours for 7 men to paint a room.

Answer 1

28 men are needed to paint the room in 3 hours

Solution:

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.

$a \times \frac{1}{84} \times 3 = 1$

corresponds to rate x hours = jobs and "a" is a variable for how many men

$a \times \frac{1}{28} = 28$

Thus 28 men are needed to paint the room in 3 hours