## 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 long and twice as wide?

12 days because the walls would be four times as big as the first room.

Posted in Brain Teasers

6 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.

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