1. Find out how long it takes each painter to paint one room.

• If it takes the first painter 4 hours to paint one room, then first painter can paint 1/4 of a room in 1 hour.
• If it takes the second painter 2 hour to paint one room, then the second painter can paint 1/2 a room in 1 hour.

2. Next find out the combined rate at which they can paint 1 room.

• 1/4(x) + 1/2(x) = 1 (times each of the rates by x and add the two rates and set them equal to 1)
• 1/4(x) + 2/4(x) = 1 [change the second fraction to 2/4 by multiplying top and bottom by 2 (this gives a common denominator of 4 so they can be added like to like)]
• 3/4(x) = 1 (add the two fractions remembering that only the coefficients in front of the x are added)

3. Multiply both sides of the equation by the reciprocal of the coefficient in front of the x, and cancel. This will give you the number of hours it takes for the two painters working together to paint one room.

(4/3)*(3/4)(x) = 1*(4/3) (Multiply by the reciprocal of the coefficient)

x = 4/3 hours (The multiplication on the left side gives you 12/12 which equal 1, 1 times x equal x. The multiplication on the right gives you the 4/3 hours.)