## Painting a Bigger Room

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.

9 Comments on "Painting a Bigger Room"Mark W Allen says

August 19, 2017 @ 00:28

Do you mean a room twice the size?

In which case, the walls would be 8 times as large, unless I’m misunderstanding your question:

Twice the length = (3 + 3) + twice the width =(3 + 3) + twice the height = (3 +3 +3 + 3) = 24 days?

Love your puzzles, btw!

Dan says

August 19, 2017 @ 19:58

You’re right, the dimensions should just be width and height, since you only paint the walls, not the floors and ceilings.

Lalit Nijhawan says

August 20, 2017 @ 00:59

12 days

Vishal Garg says

August 22, 2017 @ 00:24

I think some confusion is here with the question. If painter paints a room in 3 days that means he is painting 4 walls in 3 days, for simplicity, if we consider that he is painting in 4 days, then we can assume he is painting 1 wall per day. Now the size of wall is doubled, so he will paint one wall in 2 days. That means he will take 8 days to paint all 4. It can be concluded that time is doubled (4 to 8), so he will take 6 hours not the 12. Please correct me if I misunderstood.

Drew says

November 27, 2017 @ 18:45

I disagree with the stated answer… Unless he’s painting floors… If walls, then he paints 4 of them (the perimeter of a square) in 3 days… Doubling the width and length of the room may quadruple it’s area, but the bounding wall would only double in size. So it would take 6 days to do twice the work. (Btw… This is one SLOW painter!)

Dan says

November 28, 2017 @ 09:46

You are free to disagree, but it’s basic math. If the walls are 10 ft x 10 ft, that’s 100 square feet per wall. 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 400 square feet, for a total of 1600 square feet to paint, or four times the initial area. Thus it will take four times as long to paint.

J J says

April 11, 2018 @ 00:27

If the walls are 10 ft x 10 ft, thatâ€™s 100 square feet per wall. Four walls makes 400 square feet to paint. Doubling the width of the room makes two walls 10 ft x 20 ft. Same for the length of the room. Notice the height if the walls don’t change. This means each wall is 200 square feet, for a total of 800 square feet to paint, or two times the initial area. Thus it will take two times as long to paint.

Dan says

April 11, 2018 @ 10:12

A 10′ x 20′ room is not twice the size of a 10′ x 10′ room.

J J says

April 11, 2018 @ 12:54

Let’s try again.

A 10’x10′ room has a perimeter of 40′. A 20’x20′ room has a perimeter of 80′. Twice as much wall, twice as much time.

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