A painter needs 3 days to paint the walls of a room. How long would it take him, working at the same rate, to paint a room that is twice as long, twice as wide and twice as high as the original room?

Question

A painter needs 3 days to paint the walls of a room.  How long would it take him, working at the same rate, to paint a room that is twice as long, twice as wide and twice as high as the original room?

Reiny · Answer

we are looking at the surface area.
so each wall is four times as large as before. (eg. if one wall is lw, then the corresponding new wall is (2l)(2w) or 4lw)

So it would take him 12 days

(BTW, I could paint that room in 3 hours).