A painter needed 3 days to paint a room. How long would it take him, working at the same rate, to paint a room twice as large (twice the width and twice the height)?
12 days because the walls would be four times as big as the first room.
If the walls are 10 ft x 10 ft, then each wall has 100 square feet. Adding the four walls makes 400 square feet to paint. Doubling the width and height of the walls to 20 ft x 20 ft means each wall is now 400 square feet, for a total of 1600 square feet to paint. 1600 ft is four times 400 square feet, thus if it took him 3 days to paint 400 square feet, it will take 12 days (or four times as much) to paint 1600 square feet.